Projectile motion is the motion of an object thrown into free space that moves under the influence of gravitational acceleration only. For horizontal projectile motion, the horizontal component of velocity remains constant throughout the motion, while the vertical component changes due to gravity. The time of flight is determined by the vertical motion equation h = (1/2)gt², and the horizontal range is calculated using s = ux × t. For angular projectile motion, the initial velocity is resolved into horizontal (ux = u cosθ) and vertical (uy = u sinθ) components, with the time of flight given by T = (2u sinθ)/g, maximum height by H = (u² sin²θ)/(2g), and range by R = (u² sin(2θ))/g. The key principle is that horizontal and vertical motions are independent but share the same time parameter.
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Added:ever do. So from today you start reading on it. Now watch this. Watch this.
They will give you a question that needs you to apply the concept of instantaneous veloity.
I know that there's an easy way people will write this word instantaneous.
If I tell you you know the speed of a body but if I tell you what do you think of see expression science what do I say expression is science that's one thing I learned early as a person that a good scientist knows how to express because for the fact that I said something that's what I think about does not mean that it is wrong and you that you learning what you read in the book does not mean that that one is the correct One day a matter of time we know. Do you understand? So based on your knowledge what do you feel is meaning instantaneous velocity.
What do you think?
Just try.
I know that you might be a man of very few words.
Come on. You can just say it anyhow.
Just >> I'm touching.
Oh, thank you so much. I said I was in my mind when I was like, "Hey, thank you so much.
Thank you so much."
All right.
God bless this boy for me. And it was yesterday. I not my lady again, bro.
something changing now you know is inside you you understand the position vector of my wallet when I start with you your certificates you know so that you said if you check any textbook that you said they must write have you read before you seen before cuz that's how to say it that was too direct but now let me tell you how to bring it to make that state look like it never existed. Okay, you may ask which of the is true of instantaneous velocity. You now see let me just take the correct one so I do not mix up things.
Instantaneous velocity is also referred to as the velocity of an object in a period of time where change in t is z. Sometimes you say the velocity of an object at a point where the t you know the t means change the t the t is equal to z. Can you justify that statement?
Who can justify that statement? Let me write it out. I said we said so we said instant velocity is velocity as a specific point mean now and I told you that as an A level student as an advanced physics person the proper thing you should keep in your spiritual body about velocity is this statement velocity Instant velocity is the velocity.
Velocity of a body and interest at a point where the t is equals to zero. Sometime they will say at a point where the limit of dt approaches zero.
Can you justify these two statement the same because he said look at statement deep and justify can you transank your spirit or a voice spoke to you not know the one that is doing you know one of the two is doing you if any of the if any of the two you need to check whether they speak to you check what do is not the right it is looking for think about it.
>> Thank you very much. Now see when change in time is because you are saying that it's happening where time did not change there was there was a consolidation of time we took it as a region where we cannot describe where time passed not because you have to post an event and measure time and say that is this time I want I don't want a donation because the question means no donation you know there Time is duration. Some people measure time measure duration. What we are measuring, right? It's both time and duration. But in instantaneous velocity, you are measuring exact time not a duration.
That's why I said velocity time. Time is a specific time. No, it's a duration.
I get what I'm saying now. So specific time. So don't forget it. You understand? Don't forget.
Now it means that if they give you something like this velocity as a function of time that's when they put velocity as function time is equal to what?= = 3 CQ + 4 C² - T something like this.
Find the velocity of the object at a time 2 or at a point in time where t= we don't want this.
Now watch V like this. If they tell you find the velocity at the point where T is equal to 3. What will you do? Everywhere that you see inside here what we put three four 3 into bracket 3^ 3 plus 4 into 3^ - six here I would like to define this event in the next form you define as so 3^ 3 is what 27 * 3 is what is 1 + 3 27 * 4 is 12 bless your eyes 3^ 2 is what 9 * 4 can I see you see you created a bond between yourself and I read up at the end of the use of use and use explain this briefly.
I the more you use an organ body the more advance the less you use what we have to do is no not only it will go forever.
Yes, you become vestig.
So that den that's your brain.
That's your brain. Seriously 9 * 4.
>> So why because you check that one already 81 + 36.
God say I don't know you want to press that one 14 now you don't like so 114 that is as a type See based on this function this person was moving with this speed of 114 m per second that person will be able inside the street.
Now that's for that.
Now what about conditions where they did not give you the velocity function? Let me show you. Let me show you how how you can advance your ticket. They did not give you the velocity function. They gave you the position function. They told you x = 3t² + 4 t² they told you find the velocity find velocity at a time= to 2.
What are they asking about?
Instantaneous velocity. But they give you the velocity function. But can we get the velocity function through what process?
>> Differentiation. You are getting it.
What are we going to differentiate?
Differentiate this personally. When we differentiate what we get v= dx dal to what 3 * 3 9 we subtract from you? 2 plus what do we have? 2 * 4 is what?
80 was one two of us we have got the velocity expression now we can now limit time to be equal to what two time put what inside two n open bracket here two plus brackets I'll tell you something about the psychology very soon. So vers 4 * 9 I'll tell something you and I see I supposed to watch 8 * 2 >> 16 30 + 162 >> 52 should I tell you what you did I did because you know that I will come for you you are now more focused in the future of the class you were calculating this on around.
>> Yes. See, you you that's the best thing. When you're in a class, you're supposed to be in the present and also be in the what? In the future of that class because student is a student that already the end of where class. So his name stud If what I'll bring out one to 10 question is an exam exam.
You see that this knowledge you can score everything in that part. Now 10 marks you score everything in that part.
That is knowledge. Once you know you are doing that is knowledge.
It's not now.
Now watch.
We've understood instantaneous.
There is something now. You know the one we are done now. We have been journeying from where we learn that journey through different. We now know that we move from position and displacement to velocity will differentiate from that velocity to accession. We do differentiate that.
Now let us now find out if we have acceleration equals to 4 t + 3 t² - 5 t if you have this if you have this and tell you find velocity function you want to get velocity function what you do integrate now everybody One of the biggest lies that your your teachers made you feel in secondary school.
How many of you? You do for hours if you invest is you I'm looking for why you had that nice because of the back now and which one is easier then mass Even the most serious which one do you feel was easier the truth is the problem was mass they to m they not treat father mass they don't to do all this the boy was 2 years older than your grandfather to pick up became four years older than the son. What is this?
Come on.
I don't know. But you got you got you got the probability.
>> That's my problem. to be organized is your problem.
V is equals to what? Now if you want to integrate what you do three you know that if it was different what we do if it was 3 * 4 thenus integration just do the opposite you miss out big time you miss out we just getting a free course do when you do this on one process all you need to do the opposite is the other process if You learn different understanding.
Yes.
Yes.
See v= to in this one you + one. After you plus one add those things together.
What you do? You will not divide this by that one. This what I did. Repeat again.
This one plus one.
This one invisible.
You what? Plus one. Now two. Is there another thing here? Again. When is there you write plus C.
If you not C wrong.
This C is your past. I'm not joking.
plus C is the initial if this okay integrated the answer is that C is my initial velocity so sometime the question I told you that initial 4 and you finishing I don't put that until you don't do you understand I just said so I don't think I joking the C is a past ar.
So what's behind 4 C 4 + 3 T3 / 3 - 5 C² / 2 + what? + C.
What is the initial parameter? It is the past initial forecast from this tal plus what? T3 minus what?
>> 2.5 t² + c.
You get there.
So now let us try something.
Let us try something and see how it works. What is the thing you want to try?
Let us try and solve a question.
The question will be a question that they will give us velocity so that we can try two ways. understand what I'm saying. If I relive motion and I want to get something about position, what will you do? Integrate backwards.
But then if I want to also get acceleration, what do you do to the velocity differentiate? That's put you in so that you can take me forward and back. Do you understand?
Now let's say velocity is equals to 5 t 4 54 + 3 t 2.
Mhm.
Now we tell you a find the velocity of the object at time t = 1 second.
B find the velocity t at a time.
Find the acceleration at the time of what?
And time t = to 90 1 second given okay you don't use given option C find the displacement displacement After 1 second given initial position, initial position is 2 m.
Who can tell me what is your plan in this? What's our plan? They've given us Velocity expression.
What they should get in the first one?
Find the what?
>> Are we supposed to integrate or differentiate? No. Because they gave us a velocity function. The last time we should do what?
>> What am I just going to be doing to this place? Put what? C as what? one and so is that the case? Then in this one, find the acceleration.
Find the acceleration at a time equals to what? 1 second.
Somebody tell me what would that be?
Thank you very much. You have no you see you've gotten it already. You have to differentiate the what? Velocity. Then when you get the answeration what are you supposed to put one but that isation you can put the one last find the displacement what likely velocity to get disment integrate if I integrate this thing the expression gives me the displacement what do you mean after integation I told you that something that you see put at the end see that is why at the end of this he said giving initial position is written 2 Let's fire on its foral position.
Final position don't just stop what you get and we told you after any with one.
Should I tell what makes you give you questions you you you panic you you in fact you by go and look for what will scare you inside the question. Some of you have phobia for alphabet like eggs.
If you just see X everywhere is not good again.
You have the right to carry your paper.
Change it when you're done. Car, close your eyes and write it back. It's not supposed to >> is true. Let me see the velocity.
Leave velocity.
>> Okay. Eight. It's easy. Now is one.
>> Then this one. Do it.
>> Please.
One.
This is just C5 plus.
Yes, it's plus C. That's 1 + one. Okay.
Good, good, good, good, good. Then do you add the last two at the end?
>> You see it?
You did not instruction when you are done. Immediately you finish. What are you supposed to write? Plus C.
>> Okay, so the answer is false. Sh.
You understand what we're doing? You like to be careful.
Understand? Men do things carefully. We don't rush.
Take your time.
But you can't take the time.
202 on YouTube.
I'm somebody that's take your time and finish at number at what time?
At what time is velocity zero?
Think about it.
Huh?
I feel like I should go.
the question = 5^ 4 plus This is power.
Carry any of them to the other side.
2T will cancel 2 out of 2. Take the square root give you of a negative number which is the compressive number.
I'll show you what I mean.
H not posing it.
So I started I told you that time I told you that I said I don't get it.
I never do it. Try it. Try it.
My phone.
I look All right, YouTube.
Okay, let's continue on without time.
This is almost 17 minutes.
We need to talk. Where are you? What is you? Where are you? What are you doing with your life? There's a question I'm trying to ask.
motion itself how we can apply it into motion what I'm saying and it's not complex I promise you it's not it's just hard for you something you guys well not it's not complex you know complex and hard art is depending on what you're using to write it like paper on something like it make it hard but complex is about what you are writing the ability to understand But that's why I like using short paper to write.
Hey Okay.
Well, don't be So now imagine imagine motion What letter was this call?
I know this was about the two dimensional motion of object in free space.
But do you know that? Let me tell people about you know because one thing is for me not to tell what you did. You understand what I said?
What you hear about is a body part smile.
They told you to stand.
Now what is the only one where you have to prove to that truth you're not serious and once you prove it before you put your key What?
Nice one.
>> No, we take time that is one of the character of It is telling define projectile motion problem. You can measure part because that describing the projectile the object exhibiting the parabolic motion is projectile. So how do you define it? Right? A projectile is an object thrown into free space.
is an object thrown into here space projectile free space into free space and allow to what is No free space the movement we know that comprise of a rise and fall. So it went into space is allowed to move under the what influence of gravitational acceleration only.
You see that most important partition because some people of gravity every acting on you nothing else.
Do what?
What?
You understand?
That's it.
Now, now there are three categories of systems.
This one I vertical projectile as I just go and my parents but unfortunately as I was anticipating it so that then I treat like this.
If I treat like this, how can that question forever straight?
Okay.
So it makes things wonder that time was there was no component of velocity.
There was no component of vertical velocity.
It means they only propagated it with horizontal motion. It only had vx no vy just moving. After gravity gravity starts to ground that is horizontal. We have another one that will throw up at an angle that is angular projector. Then we have one that like an incline in what we call angular on this.
Are you understand?
projectile right it is the motion of an object projectile you know I don't projectile projectile in the by projectile motion your definition you can reflect parabolic parts do you understand Because we have any kind of motion and some motion are called conical motions project is one of the conical motions because a parabolic motion you can par this for this parabolic motion in the motion of a move this direction is parabolic but it's not projectile. Yeah, you understand not all projectile motion.
You have another one hyperbolic motion motion.
Example is when comets are trying to strike on the earth, the earth causes them to deflect. They deflect hyperally.
So if you can reflect the parts, the nature of the parts. But here projectile, they're talking about the object you do.
It's not someone that's how God wants you to be projectile. This is an object thrown into it.
Sorry, I just remember something called the people.
Don't cancel project.
This is an object thrown into free space.
are allowed to move under the influence of gravity acceleration only. Please underline this gravitational acceleration and only Those are the key words in it.
Those are the key words in it.
We go back and now horizontal projectile vertical Cap the time angular angular Oh, wait.
What's the height above the ground?
horizontally at the height above the ground.
So uh that's why I say this is the motion of a body vertical horizontally.
from a light.
I move on the ground.
Is that something?
This motion of the body th horizontally from a height above the was the ground.
Are you following me? Now see how the motion will be and let's study the motion together and bring out because you need to do it one by one.
You treat one motion you understand that motion you go to the next motion.
Don't jump back once one by one.
This is general for this motion.
Now this floor from this height the P will be thrown.
It will go straight.
Now, now you throw this like this. This guy goes like this.
This thing, this place, this line goes, this line is only showing us the direction of the velocity. U is initial velocity propagated like this. Do you see any velocity? No. This body only strang which was the actual ux ux or component velocity. But this guy the the meaning of this at the beginning of this motion is u y is there anything like u y u y= to what? zero because the person who threw not bend you still see some part of the motion >> chief down.
So now because small component of what of velocity but like this now but like this now it is giving only horizontal component of what of velocity.
only component of velocity and so therefore it will propagate horizontally initially and because of gravitational field that is acting and surrounding environment this guy start doing what bending down like this bending so eventually when this guy is striking the ground is it striking the ground with only horizontal component velocity no he has gained vertical due to gravity as he was So when they horizontal as usual, let me tell you all projectile motion does not change. It does not change. If you were 10 horizontal initially before when you get to the end, you shall be what? 10.
So that mean we have X here and the value of UX is whatever Z was in this place.
Dear What you said is not li but like you said dynamics can studies The motion is in dynamics that will study the force. All the things the person had to come create even the bouncing up is still caused by we call it impulse. You understand? We call it impulse. We call it rebound due to impulse. There will be a change in momentum. So the first rebound might be like this. The second rebound will be lesser. True.
Who cares about if you know let's not. So this place now before before the band something you have ux and down here you have what?
>> Vy this one is vx it's just that we know that vx change it still be the same as it was before value.
So if I ask you calculate the velocity with which the object strikes the ground. Calculate the velocity which the object strikes the ground. What I do that square<unk> v y 2 + what?
That is the total velocity.
Do you get this?
They will also ask you calculate the impact.
Are you getting now? Calculate the impact angle. The impact angle. What do you mean by impact angle? Impact angle is what? T equals to component of Y which is what?
What's component of Y? Component Y is what? dy over compent of x bx to carry this tan to this side. W= tan= to tan inverse of dy dx you know the do you know where you find the is the difficult things in repetition when you Repeat it first time and second time you solve 20 question one morning.
You know the one you just have as a student one morning you just wake up motivate one kind food be cooking you will not be spending you just see this morning somebody yesterday I just just read you can life every day it's little little changes that you get me result that's small before I just 10 questions 10 only 10 before I eat every morning. You see that small tiny habit what it aggregates you become is immeasurable because it will not only your life it will your goals your ambition your character your discipline everything the truth instead of lying to yourself complete 24 hours 24 hours what I want to read 24 hours to read that's not I'll continue to promise you.
Let's go.
Is it cool?
It's good.
Don't think it too much.
So what can I do?
It's not you know this minute of blackout.
I was expecting it. I prepared for it.
So let's go. So that's all for that one. So this is how to calculate the resultant velocity.
So that's it. Now please let's recalulate something. The rules you need to remember when studying this motion. The rules, the theoretical rules you need to remember what at the initial component initial component of velocity, the vertical initial component of velocity is what?
Zero.
What did I say about the component of x component of velocity all through the motion? What did I tell you? It does not change. It remains what? Constant.
Are you getting me now? Then hope you know you know those equations of motion that's what you come to use here let me explain what I mean by that V equals to U plus or minus you know those things now this for is just that we treat them separately for different components if what I'm looking for for example they ask me to calculate the height or they told us that we should calculate the height from which it was thrown the height from which this object was thrown Are you going to be using horizontal component of motion to calculate height?
Everything that will be in your equation of motion should be about height. That I'll pick one of the equation motion and I will do something that callition. I will circumcise the equation and make sure that everything inside there is only height parameters.
Let me show what I mean. Imagine I pick V = U + 80. I will change everything here to b y equals to what u y plus or minus I will tell myself acceleration is what gives horizontal motion which one gives vertical motion g I'll come here of a and put g and time is irrespectant is not a respectctor of your dimensions of your what do you call it of your direction bro does not Your bro is just counting. If you like password, you keep counting. That's why they say it is the what? That is what bind event.
Time is the distriution of event. It's just there just distinguishing everything. You understand? So let's go on. So learn how to extract the equations you need. If they ask us for instance, look at let me see if you calculate the range. Range means horizontal distance. Calculate the horizontal distance from here to where it land again here that's like S call it S we call it what will you do what I tell you go and look pick on the equation of the motion that you feel work and let me tell you from experience I will say this thing from experience I will say it any of any of V and U it does not be useful when you're calculating range what I any component any of motion have V and U and you intend to use it and calculate something that has to do with distance or distance it is a waste of time is a useless equation for that moment should I show you why so we said the horizontal component of does not change all through the motion so that means we're saying ux and bx will still be the at any point in time. So if I pick equation like v= a see what happen what is going to happen that the u does not change that ux be the same value as vx what I do subtraction is equal to what it is a very useless equation so there's only one equation see what I'm telling You pray after playing as reason speak in tones while you're playing. Speak in tones. Let it sink.
Watch.
It's only this equation I know that works. S for horizontal projectile. S = U + A C U C plus R A C square because X is actually what horizontal what horizontal distance we're looking for U is that UX T is something but you will be zero If you can get this while it's zero, I will look for my post and I'll wire you transfer. I'll shock you.
I promise again.
Serious. See, just tell why we time is going. You not believe you what you know into your account. Eh mm you're almost there. It's just it's not as if it's supposed to be you know this vertical and horizontal component of stuff this thing now it's about mm that's not it this place will not be there again because of something is about this thing do you know the answer god God you bless me too much that even when I want to waste money not to waste what love don't worry Let me help you. So the reason that I said that what did I say when the body is thrown into free space only moves under the effect of what gravitational acceleration every other is equal to Z. So does it make sense now? So it means that this a= 0. So multiply everything.
So what do we s= to what? Uh no no no what my trans you will see you shot. You will not as that he went to go that's why you come down.
Let's go.
Now if they told us now that this tower the height of the tower was 45 and the tow 45 if I tell you that let me tell you something there's a gift I want to give you for horizontal projectile I there's a gift I want to give you projectile it happens in other projectile too but since I'm doing this say any question that asking has to do But there's one new thing is doing what university there's one becoming before to do it before that time was but it's like they reduce their hand on the student but have been doing it since schools what was that now they don't like stone landing on the floor again it's as if event every time and somebody cut the stone at 12 times Because of 4 seconds on the floor it's because of question like that bro anytime you see any question like that the only one you have to move first one and that is you don't understand time is not confined by any of the directions there once you can know the time it takes to move from this place to that place has finish you can do that.
So the best is go and find a way to know time it takes to get there. Once you know the time to get there maybe there once you know the time to get there finish I tell you and there are many ways to know that you can manipulate how you get it. I will bring out two questions like that I'm done with this one two you will see for yourself how easy it is to finish exams. What does it mean all this? You will see what will tell you calculate his height 2 seconds before he landed on the floor.
Don't worry, let's go. You will see it now. So, I wanted to do an illustration.
Imagine I imagine 45 once they g you the reading they don't need to give you anything again the only need is your brain you can find the mean by yourself should I show you if they give you one give you height or give you width the mean horiz let us solve the project now let us start let us know all the events so to get the time I'll use CH = 1 / 2 GT² do you know this before Good. My question for you now is not the formula. My question is this formula comes from somewhere else.
I mean I know this square= I don't think but those two places what see something h is equals to ut + half gt² that's the difference between this and this one I wrote is that this one has appeared I said but what made this disappear they don't just leave they don't just leave relationships because this is a relationship. They don't just exit relationships like that. What would they do? There must have been a reason. Now watch what did we say about you know you know expression make sure it is in the direction dimension of what you want to work with since I'm working with height that I'm working with vertical parameters. Now this U I want to U Y two of us this G is already showing vertical parameter I mean what is UY from an horizontal protector thank you very much so if you put Z * T that's why I left with this many student come and try this one then they will not exam question like which of the following expl this expression by a because the vertical component of this one is this vertical.
So please pay attention. So can I get the time from this? Now that I know that the height is 45, I have 45 = 1 2 * 10 * t² 90 * 90 = 10 t² by 10 t²= to what?
>> 9. So that t= to what? 3 seconds.
It means that the time it took the object move from this beginning to this place for seconds 3 seconds.
Let's not again that want to know what the horizontal range is. Want to know the horizontal range? What horizontal range? X= U + A. What I tell you circumcise the equation make sure you express the pariz ux to show that I'm only working with things along the what x and a is also an acceleration along the what x it's just that in motion see we get a a there's no otheration aside from gravity it means that the of this place do come Do you understand? Because a is a bad boy in this TV also lost for joining the workers up.
So that's why you see that eventually the relationship now is s= to s.
Are you following what I'm saying now?
Are you follow I'm saying now? So this is what we can use to get our age because we use this one to get high.
Do you understand now? What's the time to for him to get >> 3 seconds is that same period of time that broke over this height and still cover this distance but within 3 seconds it got to this place.
So we now come and say S is equals to U.
meeting with you. That's where it do you understand? Let's imagine that they projected 10 second per second which 30 m sorry 30 m.
Let me share with you the kind of thinker I was as a point in my life.
You see this thing this topic I almost never understood it not because of anything but because my brain didn't want to allow me. The question I ask is sir how I want you to change this time for vertical and horizontal.
How come to know that the vertical I used to our second society?
Then I now came to realization that the event happened simultaneous.
That means there was a time they were both happening together at the same time year and year. That was how they moving coordinated with utmost understanding of one.
You should have answer.
Are you following what I'm saying guys?
Hope you understand this what I'm saying.
Good.
So the final answer is 30 m. Let's imagine that I told you told you what what is the velocity? But I told you an object calculates its velocity at exactly one at exactly uh 1.5 seconds from projection.
Did you know the distance exactly 1 second the projectile do you know they're telling you that imagine when you get when moving when you get to 1 second at that one second time what was his fellow do you what I'm saying now so look at what we now do what we now Good.
This one's a my life. You have to watch this time.
Yes.
I watch this movie.
Now watch what I say what calculates the velocity of the object at time 1 second so we don't want to know I don't want to know the drought Pick an equation that satisfies the presence of time. This type is what they use to define the motion for you.
They use the definitive entity that give to you.
So how many of us my voice my voice is the voice? Okay.
So, so, so now watch.
I'll say something. One second. So, we come here now. We say we say C.
We say C is equals to 1 second. What do we brother component always there is always there any type of loss just sometimes you just realize that he found you before you found him so g is equals to 10 m/ second there are some set of people I respect in my life those people 9.8G 8 since we did I don't know why they have that patience suffering 10 when street 10 now watch see G we know that one guess one again that we know we always know what happened at the beginning of the projectile most times What is to protect the body? You and those things. What is that one? Take advantage of the things you know.
There people script when you see them you'll be angry. They will break the projector into parts. Project all the way from the floor to the roof. From the roof to the window they now start rejoining the capac.
No, no, no, no. I've done that before in life.
I found that it was hard work. Study smart. Let's go.
So, what am I having?
God bless you. You caught that. U is equal to what? 10 m per second. But you know, it's wrong for me to write it here. Guess what? You know everything I told you that in this in the rule of make sure that your parameters have they obey the rule of resolution if it's Y component you are writing let it be only Y component like for example this U as 10 know for horizontal since I put J in this place it means I'm only writing things for vertical for what vertical now brother will come off The correct person to come there is the vertical component vertical initial component of Y that's UI it see and that value is what >> 0 equals to 0 m/ second when I was when I was secondary school that time I used to turn the question to go like this I turn it to go like I can eas that time. So I just that's like saying final velocity based on that time that time last time.
So I'll just call it V Y because of it Z equals to what? I don't know.
Do you get what I'm saying? Brother, are you still with me? Sister, are you still with me?
Well, what I connect all these things V u GT V Y equals to U Y plus what? GT.
Are you with me?
me after she spoke a word then what do we have able to do your intentions >> vyals >> = plus waiting bg >> waiting in T >> Val I put plus you looking at it 10 * 1 is what >> what do you know the meaning it means at exactly one second if this exactly 1 second e If this place here, if this was the place that was 1 second, eh, the vertical component would have been what? 10 m per second. What will be the result component? Somebody hit my life.
>> God bless you. How do you know?
>> It's constant. Hey Jesus Christ, it almost fell down. Is that I swear?
Hey, God.
Please not this.
So what do we have?
The last be massive online. Hey, he broke two records.
respect.
So brother help me what I so that means we now know that this point here is also what?
So we have this 10 m/s 10 m/s.
What can we get from there?
You now have the vertical component and horizontal component. You get the resultant. What's the result? Tell me is equal to what?
square root which gives us what it >> okay 200 >> God keep it tomorrow what is the value what's the Okay, since we don't know the value, I can just put I'll leave it inside 200 250 225 like your brother. I to break it down.
This one take two. This one take two.
This one tell you nice same thing. So that means the result is equals to what 2 is 0.7701.
So the answer is 7.7 now I feel.
So this is it.
Hey, are you serious?
>> R2 is what?
>> No, press two for me.
Okay.
>> It's one that is 0.70.
True.
comes before 14.
So can we get our scan? They will tell you they will tell you find the angle of impact at that level that 1 second impact is the angle of impact. It's just to say tan theta= to vy >> 10 / 10. This one if your computer don't believe me again don't believe me again 45° press it now to to validate me slow.
>> So let's go there please. If you finish and you leave your answer like this 45 for something like this they will not mark it. Do you know why they not mark it?
about direction quadrant is important.
This thing when you do like this is 45.
Do you understand? Complete the quadrant that is 90 + 90 + 90 this part here which is also 5 or you see 360 - 45 360 - 45 is equals to what 350.
So that's it.
Do this.
What are the rules? Just remember, take advantage of time.
Circumcise your equations. How to make your equations if you only understand? They just know what governs that particular type of projectile. Is that clear? Yes. Let's move to the next one. Angular projectile.
I want to do everything.
We buy water for the night.
Okay.
I guess I'm talking about zero.
>> Very good.
>> 118.
motivational no.
So now we're entering angular projector. Let me tell you something inside angular projector. The same thing is happening. The only difference that at the beginning we had vertical component components that horizontal component remain the horizontal component from beginning to the end not change horizontal components know the change and the gifts God give us in that that's if used to change much it's Yeah, that's okay.
All right.
Okay.
See Now that projector, the object, the object, the object used to move from an angle and land in another angle. example and again again the symmetrical is what symmetrical so I don't think you need that don't wor because there some kind of projectile angular where we will not neglect and giving us unymmetrical results So, so imagine we had a ball here like this.
So, my sister needs What was watch?
It's not show the camera.
I have Okay.
This thing easy.
Don't like that. That was what projectile we did. Was it difficult?
That was another project that we did.
Was it too difficult? It's something that you know that you spend more time writing it. That's the most difficult one. I started with that one. That's the most difficult days that breeze just breeze. Seriously.
See three things are general from EFS. Three general things exist here.
Those three general things are the ones that are commonly everywhere. People know what are the horizontal projector the time of flight. Calculate the range. Calculate the what? my small all those ones that's the outside of those ones believe me the remaining sib you know you fine Bless you.
So from here the object will be projected at an angle.
Let's call that angle angle. Angle theta.
My brother the first thing you do see the problem of Nigerian students in this angular this in this angular period time is they've taugh them three formula it's like after the person so because of that their mind just closed on this topic once they done because sometimes or five time of flight range maximum Yes.
So after this guy laughing cannot do again she knows like I know anything like with what velocity did this strike the ground they're not going to do it with what angle angle of impact does it land on the ground they will not touch it if the object was caught at so so second what velocity was it possessing as the catcher all those words for the examiner there only three now I'm going to assume you know those three let me those three first those three because they are very important I of flight equals to what good but now let me tell you something the fact you said the formula that's to tell you this that you know the formula.
Do you know brought about the formula?
I call it formula circumstition. You see always learn how to enter that two dimensional something. Always learn how to break that up into it components.
Always break it up into it component.
Have the one for xaxis. Have the one.
You understand what I'm saying? For instance, see something. For instance, now for instance, now we have we have Y, we have V Y, we have U, Y, we have G, we have T, we have H. All these people, they are family members.
That's what I'm saying. They are what?
Family members. Do you know why?
All of them are describing one particular type of motion. What's that?
Vertical motion. vertical component of motion. Are you following what I'm saying? Then we have another one again that we call what? We have what?
U sorry is correct. Vy U. This one V Y >> VX UX. Instead of G, we call it A.
C is not for everybody.
Then what's the last one? Sure.
So I never have a reason to in one formula one me there. That's nonsense. I'm using one one of them there. It's nonsense.
Once you can dissect the formula of two dimensional something like this you've hacked you've you've projected people wondering how you doing it they think they just think but and when they see your workings the fact you know you go long walk you just know and sh now watch I want to show you why that you know the equation of motion.
I told you earlier on that inside equation of motion that for horizontal component is only one equation that we have that is useful because that other two you know velocity do not change if you carry velocity other side it turn to zero when minus I told you that so let's start with maybe h how to moment or I can anyone let any time of flight anyone goes v = to u + minus gt you see I'm careing something v equals to what u minus gt Are you following me? Now that I have done that one, the next thing I am going to do is this. Watch me carefully.
I'm going to express these people in only one family household. If that English exists, let's use it now. Sh is a type of flat I want to get.
I can use any of them. That's the truth.
I can use any of them. But before we proceed, let us resolve this vector to the vertical and to the rear.
But vertical can be changing.
What would this place be? You what?
>> You sign you know why sign this one? But you was doing you I follow you season.
So we are there.
We are there.
Watch. to express everything. Express everything there. Now v what is this? Vy equals to what? Uy minus what? G C you go. Now watch. I want to consider see I want to use parameters from here to here. From where to here? from here to here and I know that at maximum height here what I'm going to speak I hear it well at maximum height velocity is not zero do you hear what I said at maximum height velocity is not what >> zero >> what is zero vertical component of velocity is one is what zero so in this place where the motion is coming when you get to this highest point we will still have horizontal component of velocity that's move it as if we swing it to that side but do we have vertical component of velocity no that at this point vertical component of velocity I can call u is equal to what z you understand so obviously if I study motion from the beginning to my maximum height what will be my vy Given that vy is my maximum position y no it will be equal to z before sorry please pardon not zero okay okay not for this equation okay see where we are me no so This way we are doing it. Now what's our vy to maximum velocity maximum for vertical component is z= what's the result component?
Thank you very much. U sin theta minus what gtus gt= what u sin theta. So divide both by gide by g= to u sin theta / g that projectile especi so that what happens in the half side physically re are you get what I'm saying so what am I trying to say If from here to here the time to get to this place from here if the time to get maximum height is this what will be the total time of flight together.
Thank you very much this one now. Okay.
Okay. This one now is this. So we is no no t will be equal to 2 * get to maximum height which means t is = 2 u sin theta g.
Am I okay?
You're doing all this with your book.
Yes.
Uh Okay. Okay. Okay.
Might the Lord grant you grace to follow up. Say amen with this. Let's go.
This is the problem for maximum height.
>> Time of flight.
Oh yeah.
See something.
We now have what now?
V.
We have done this one. Want to get time to get to maximum height. Time to get to maximum height. That one I'll be having h is equals to u y t + half gt² u/ t minus/ gt² are we there? So h= to what's our uy u y initial initial component is u sin theta initial component of velocity u sin theta it is the maximum height to u sin theta what >> c + 1 all Huh?
>> Okay. Minus minus what?
You know what? This place is a more complex place to get it from. I'm not ready to start doing what you call it quadratic equation. Be making things X and Y. Please please please please where my husband let's take a U-turn you can get it from there you can you can get it from your jokes but you do some level of with imagination please v² = v y square = to u y²us what 2 g h easy p 0 Now, now BY is what? Z Y Z plus U Y. Now wait u sin theta. So we have u sin theta all of them^ 2 - 2 g h what I'm making this formula h and k 2 g h= to what u* theta square* theta So what do by 2 2= what now? U² sin² theta / 2. Now the equation that the equation final step.
Final step.
What are you getting?
into that distance and range.
Let's go to the one now is what? That one now is V X because range is range is a what?
Horizontal component. V² X = what? U X² + what?
Two two what?
Two G S remember I said I can write this.
quiet. I said it's not quiet. I said yes.
This is because the component of the component of horizontal velocity does not change the motion. So by time I become what? So what's the best that we can use? S = what? U T + R A T². You agree with me that you will be zero because only due to gravity that we have.
So we now have what?
S = to U.
So s is equals to what is the value?
>> Nope. But this is ux u cos theta right multiply by c. Then we ask what is t cuz the full so what's for flight 2 u s g.
So s = 2 u sin theta cos theta / g. I need you to know that when you have sa sin a isometric identity sin a plus a when you open it sin let just know that this here Sorry.
I said no.
I said no.
This time and this one there sin a 0 sin a plus a.
If you want to open it a plus, if you want to open it long a but the one here is usually 2 u. This one here is sin² theta t.
So this S we call it H that's left.
Do you get it? So we have goten this one. We have goten this one and we have got this one.
Yes. So what do we do?
What do we do?
Sorry.
Now there are the situation I was talking about. Imagine I told you that you should calculate the the time of flight or the time it takes the object to get to somewhere here or somewhere the time it takes it or what at what velocity will be when the time is equals to 1. I have to check all the things. Thank you.
>> This also for so motion to solve. I'll show you how we use the rounds.
Are you ready? Let's question fast so I can go.
Real smoke.
So let's fire.
So good.
Imagine they told us an object is projected at an angle of of 60 60° to the to the vertical comma. I guess they not to calculate the velocity of the object after two seconds.
That's uh person of flight, maxim because once you once You already know that thing you just said. That's it.
I said resolve locate.
That's resolve.
Identify.
Do you get? Let me show you what this one. They told us that the body is projected at angle with 60 60° 60° together.
Now 60° what are we going to have in this year with project to the vertical with a low city of 10^ 7. So what 10 second what's the what will this place now become?
They said it was projected at 60 to the so that what 30 Which one?
>> This 10.
So what are we to do? They tell ourselves they said two seconds into the flight. So we just use the vertical component to this side we'll be having 2 seconds after the flight. So I want to find the final velocity there. So I'll say v y² + sorry = v² - ux² sorry u - gt so 10 so 1 v = minus 20 30 what?
>> Huh?
Everything everything bro said 0.5 seconds 0.5 how many is five What was you 10?
Is that 8.6?
What is it?
10.5.
V² = What's this one?
>> 30 square.
>> Okay. 25. You're telling me to >> vlog?
which is >> 24 positive.
Let me tell you something. The fact that our answer is not negative means that within that cross 4.47 47. God, I always want to go to sleep.
What's this?
You does not change. So, press one.
That one is five and 0. That's 8 points.
8 points. Sorry. 8.
>> 8.0.
So what you guys see now you know Is everything you >> everything you >> 21?
>> Yes.
Yeah.
Okay.
This is okay.
Okay.
>> Oh god.
Did you kill?
Shut up.
Okay.
Okay.
Start. All right.
We stop that examples. All right.
I've explained it already. I'll just do one on that. When I do one on that, we'll just kick into since because this we've actually finished. So, I'm going to be kicking straight up into something.
>> Yeah, I'm going something to statics and AC.
Okay, there's another one with physics.
So smile phys.
So yeah.
Yeah, we ran the example. I told you want to run example. I just remember we run the example. I did the example.
Okay, let's come. Let's go. Now for a motion, a projection that happens in the vertical direction vertical projector.
Imagine you have you know it happen to start here.
It can happen from a cliff and like now not cliff as part because I want to it can happen from the top of a building at the edge that's the clip where it can skip the top of building down beyond you I'm saying so look at this the rule of vertical projectile that is unique to vertical vertical projectile is the way you measure every projectile the takeoff plane is usually considered as our x We run position vectors in this aspect rather than your normal height duration all those things. No, we run it as position vectors.
So look at this. If I threw an object from this height that was not the floor, this scene is not comfortable with not comfortable.
has a mass of 0.6 g.
All right. So, as 0.6 g, what's going to be mass of something. 6 g. Is it 0.6 g?
Huh?
You multiply it. You convert it to kilogramide by 100.
So that say 100 plus this is 0.00 0 0 6 kilog it is cool. So it is a and horizontal this one is in equilibrium position this very say they're not just showing you how one part of the motion they're trying to tell you this thing is actually like this thing here it is some something just they don't handle it but they met it start this way like this don't let anything deceive you it's not pendulum it's not moving so for it means there is a force somewhere around there and now do you know this config did not pull arrow the air make it because this is the most irrational thing that you ever think for you to arrows and arrows will be giving you pushing.
So they will not be thinking the arrows as a vector supposed to push this.
Meanwhile, this is a field that is only positive charges that field come out from. So it means that there must be a positive charge somewhere here. Maybe a positively charged plate and they're the one that producing all this.
So if positive charge plate here then I can understand that this board is truly negatively charged. See you see a tiny sphere of this ideal position. What are the magnitude? See see what are the magnitude and sign of the charge on the ball. So that the ball to get charged. So automatically for the fact that this field is like this it can only be positively charged here because they don't produce field and it validates that this ball boy must be what negative charge negative charge receives field and then there will be a force that attract you get the question is it means this guy is the one that pulled this guy to this extent like this force that acting I be good but in life you know for every equal oppos it means that there was another force that was supposed to bring him back that was acting backward that is clearly detention clearly detention The force that one is the tension. Imagine this rope here.
I know this rope here is a tension.
Tension is asking right. So we want to resolve the vector on this rope. Resolve it up. Okay. I resolve it vertically.
Also resolve it like this.
Bring it to the middle.
Sorry.
>> Ah, nice. You mean these two collinear forces, right? That's what I was saying.
You know, I told you before that for must be acting. Now, we've ced the force, but just that you must complete your free your free diagram. You can't just leave like this. You must this is way to act directly downward.
Where's the angle? This angle if 20 it mean T what is 20 that this will be T const 20.
I've told you that before that you should not be following the trick of bic must be sign it will mislead you get you use the angle where the angle and the resultant is this the resultant this is what broke the component so since the angle was here that it was here but this could use mathematical since the angle the line between what you call it resultant and this particular one between this particular one I collect the what the cost the other one now why so resolution vector has nothing to do with do y and z ais so it means that empty it means that it means that t s 20 is the one that is equal to force and it gives us the force produced by this person. What they ask us for what are magnitude and sign the charge has finished. If we get the if we get the magnitude of this charge right magnitude and the sign on what you get the first act then don't finish you get watch.
So what's the tension? We don't know yet. We can use this ones this side to know the tension.
Mg = T 20 mg's weight with this one.
I don't already.
Okay. Kg remember I 100 kg by 1,00 come 0.6 This is gide by 1,000 1 2 3.
Now this is kg* 10 wait out and it's 10. So it's not 11.6. Okay.
>> Okay. Okay. Okay. Okay.
Oh, and this is so cost 20.
cuz 20 is what >> Sorry, I'm slow.
Sorry.
= 6.3 >> H you know have you delirium before have you have you heard of delirium del that's what don't don't be angry I'm screw bro I I I'm find I like in my head this not where face I pass the face I've lost arrangement of positioning >> this please >> I don't What was it?
2.1 is from 2.1 is that it get the question that yes the massive.
>> Yeah, but I believe you understand why I did it with you.
Okay. Nove what do you mean by absolutely >> absolutely I want to believe I talk about the beginning of section does it have to begin please teach me before I teach you doesn't have to again talking because if I'm thinking the actual beginning of is circuit is is unit of measurements.
>> So the topics started it has the beginning of which every other in the past is a very So there's no actual beginning but you understand you understand that's all you have to finish that course it's the shortest all those shortest short is one you have to be more careful about short this topic that will take more than one to 12 pieces from the Thank you.
I will go rest five time.
Okay. Now, should you tell what you do for me when I'm taking you this course?
Just do yourself one favor. be sincere at every point in time regardless of what the information is because the aspect of it is not that jammed this and look and read your psychology like even in this topic did you do it in did you do it in did you do what I You will lose them in their face.
Just pay attention. See AC circuit. You see the only thing that differentiate AC circuit from what everybody is doing is one thing. Sh the beauty of the light beauty of the light of J.
It's not J once you connect your G wire and plug it going to shake.
Have you ever seen Jens if you place your focus?
It is true like you will notice minimum vibration.
Hello testing microphone too.
So now circuit is simply the branch of physics that was the end of DC circuit. All those things are doing putting resistance or resistor. If you check after everything aside from that aspect after everything you see that the next thing you see in diagram is this meaning of that. So it was battery that supply all those things. So you can't have heavy duty gadgets in a in in a normal DC circuit. You understand?
Because whatever powering them is only producing current that can power.
But in AC circuit you you can you can have a one element system, a two element system or a three element system. I get now heavy system I'm talking about right now. Watch it. Start like this. Right.
An AC circuit. You know, let me an AC circuit is one that is periodic.
Is one that is periodic and produces is sinos form when plot on a graph produces wave fun when plot on a graph. See something it means that for the first the first is that that line is unstable in the sense that it is continuously oscillating is continuously in periodic motion. how it goes on corner goes on corner but the reason why you don't notice don't notice it is because because of how frequent it does it in Nigeria our AC circuit has a frequency of 50 meaning that it makes 100 periodic event in one second very difficult to see right that mean the light goes off like it goes up on 100 times in 1 second which is your break in USA 60 that goes up 120 times in 1 second span that is now say something have you know that you need to understand that we have things that control the AC what I'm saying now we have properties that control this section and you must do that those properties perfectly well and we use them to run. So right properties of this section number one wrong.
Well, they comprise of reactants, comma, the combined reactants, comma, indulgence.
Mhm.
Like I told you inductors reactants they comprise of reactants admittance.
This part comes in you will be simple.
Yeah. Reactance, admittance, susceptance, susceptance.
You get signal impedance.
Now what is impedance?
independence.
It's what he did.
>> Exactly. To put to put an event to stop to put something on.
So the the family people are resistance.
We release that is the function of inductor comes to be they want to create flux change so that they can correct those ones to the inductive capac which which are also members of the independence officials they have to do you get this also zoom.
propagate between the propagates between X and Y >> as for voltage and current.
making up.
Check values.
Do you understand?
There's something we call RMS which means square.
>> So what does it mean?
>> Like that like that is making you feel like a pastor.
Well square velocity and the root mean square velocity or root mean square voltage or root mean square is giving information about average.
Now why can't we just use normal average? We use average whenever the constituent of what we average is something that is almost infinite decimal can count it square.
So what does for example the one for that it makes us look at the gas and study an average motion of gas.
So the same thing happens in this blue square.
>> Yes.
But the other thing is they generally taking forward the IRS describing the motion of the object.
I do.
How about you? Sorry.
So questions do they change?
Yes.
Do you know the car change?
Do you get Do you get That's going to be the voltage.
Let's see.
The root of this represented individual is not signific What is it?
>> What is it?
>> Yes.
So this is where we platform.
But before we go to that like anytime like anyone wants to use IMS to P volage you know that one already I know it's I know Thank you.
Let's go. Thank you.
Close one.
That's one.
with course my 90°. So if so and I don't know what is and one thing I can only cost 20 understand.
So the complaint is as usual still.
Check not the same as not because I don't know.
So in the same= and diamonds.
X C.
Yes.
So circle So what's this?
Sure.
This one is No, don't don't Doctor. Ask me.
So when you have the Did I say go that also spine? Excuse me.
I don't know.
It's funny. Close.
So, so which from here. What do you have?
What do you have here?
So, the next thing I have to do is This is need to cor because of comparison.
Don't want to compare the way we compare this to compare the sign of this you understand. So what do we do?
A couple seconds.
I look as Oh, Heat.
Heat.
So, so good.
Mhm.
So this one here is equals to is equals to inductive inductive reactance.
So not so that you have = 2 pi f So these two are measured on.
So while we having X and X for inductors and capacitors also having Y and Y capacitors here inverse of inverse of that's the react react Yes.
Okay. So this is also better results from all forms of independence.
of resistance reactant precisely.
So we have this distance resistance R² + X XL X C or 2.
slow.
So yes, that's it. And you use that the power factor.
The power factor is usually equal to five which is going to be equal to x - x c² / r. So if this holds true for where x is considered to be like Okay.
Then Z 1 is equal to me which is B.
The resonance must everything all of this probably the same answer questions.
Express using my visual questions.
question.
Okay. So, questions.
This is it.
Yeah.
Are you ready?
All right.
Okay.
Is 0.08 08 inductor is connected to 50 W.
A 0.08 inductor is connected to a 50 Hz supply. Find it inductive reactance.
What is it sound?
A resistor of 30 vol.
30 ohms.
A resistor of 30 is connected.
transport a resistor of 30 ohms is series 40 ohms 40 ohms.
How many Sorry.
Find you connected to 200 volts.
You connected to 200 volt.
So what?
Sh how you think.
How did you get that lost this?
So what did you use?
use resistance.
I said is the vector is the vector of all your reactions including resistance to use your viral resistance.
This is for fun. Yes.
And as particles X as R= 40 X = 90 ohms X = 50 ohms.
supply rotation.
Then I find the independence current and this angle Yes. Ex.
>> Yes.
Yep.
What are you supposed to ask?
There's no better Let's go over.
test.
What happens?
Please.
All right. Few people are coming oral group. Oral group question is your body come down bad.
machine for school.
Um, please don't take take your last question. Let me give you Okay, don't worry.
8 C 8 ohms for R.
Then 120 you know L resist resist resistor resistance 8 inductance 120 mh then capacitors 18 microfarad determine resonance frequency quality factor Bandwidth half power frequency energy. Why you looking at me as well?
Energy then energy is you can add copper.
So your question I would just like to just pass.
Okay student question is thank you continuous Okay.
75 75 ohms resisting Chef me frequency where current is maximum.
B frequency when 30° C frequency double frequency frequency frequency remain to walk any You are beautiful. I know people that the table my table you just follow peace. You would have peaceful questions come late and thrown into class for everybody.
Okay, I've got your first the second one.
>> Yes, second one.
Mercy.
What is this?
Yes.
You don't have So what's new?
have to do. You have to do it.
You just have to do it. You're not going to do it.
So number one you're going to number one I can't turn back you finish What's the seven divine world?
I'm trying. I try That is so much.
Don't worry about Yeah.
Right.
What?
>> I am not so We're good.
got resistance at 75 ohms.
>> Mhm.
>> Inductance at 3.3.
>> I'm not reading question.
>> Yes.
The circuit contain the circuit contain restor and 10 micro >> the second containment contain 75 ohm resistor 0.3 and 12 microfarad capacitor Next one.
>> Next one. Next parameter.
>> 0.3 and 12 microar.
Determine the frequency where current is maximum. When current is maximum.
Determine what the frequency is maximum and the frequency is okay. So looking for frequency >> and determine the frequency.
So all these kind of questions when they ask you this question first thing is do you know what each of those things they mention represent the reason why you get the first one is because today I think today you expose yourself to what you know what the face angle was I was not sure you didn't even do that one but I still told you what angle was a face angle is the Um >> five that we said was equals to what >> your XL XC what it >> so like this something like this. So we ask ourselves a question.
What can you do to this to arrive at a face angle of 30?
That means we want here to be 30 to construct a triangle first.
A triangle that runs in time. Right? If this is my angle here, that is I want this place here to be what? Opposite.
And XL and XC.
And I want this one here to be what?
R.
I want this one to be R. And this place here should be 30.
But there's Fred.
There's no friend.
Which one are you seeing now? Is it for wisdom?
What is it?
I think they What's wrong with are going to work on your answer. So you can play on your impedance. You can play on your resistance. I can I'm going to put 75 here and cross multiply. I have equation one.
X A - X is equ= to R 75.
So let me 43.29 2 7 5 Okay, let me reduce the values.
2 pi f the questions is frequency where current face angle is 30.
Exactly.
So get the value 157.87 >> 57 Mhm.
>> 87.
What is this?
>> 158.27.
>> What?
>> 158.27.
>> Are you sure about this? Yeah.
capacitance is having.
So we will represent we are going to represent xn = 15 1 87 let me get what this value is coming f of l I don't think that's what this one give you like Yes.
>> So, XL is = to + XC.
So um when you calculated this L this frequency is this 83 frequency is 83.
So okay.
So what's this value?
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