ZOOM LESSONS PART 1A | RESULTANT VELOCITY | S6 MATH TERM 1 HOLIDAY | MON 4TH MAY 2026 |

Added: 2026-05-11

[00:00:04]Okay. So I welcome you back from the S6 term one. Hope it was a good experience. So usually senior six is a final level whereby usually most schools prefer to finish syllabus in term two.

[00:00:19]So that means that the two terms of senior six that is term one and term two there is extremely intense work.

[00:00:27]Students rarely find time to do some leisure activities. Those who love sports.

[00:00:34]They they usually they usually find it hard to get time for sports. Those who love entertainment, they find it hard.

[00:00:43]But that is S6. You have to get used to it. There's nothing to do. The good thing is the last level for secondary or for high school where there is intense work and intense supervision. After S6 it will be now more of self drive. So expect that by the time you finish S6 you have a certain level of self drive otherwise without self drive there will be a lot of unfriendly circumstances which may occur. So today since we are fighting towards finishing the syllabus that is why I chose a part of mechanics called resultant and relative motion.

[00:01:27]Remember mechanics is under the compulsory part. Those who did the preest some schools got a chance of doing pretest you need preest questions. Yeah. But those who didn't at least you have to know that mechanics is mandatory. There is no way you can run away from it. Previously students could look for a way of running away from it.

[00:01:51]So they could do because there are three section there is statistics and probability.

[00:01:59]Then there is numerical methods.

[00:02:03]Numerical methods. Then there is mechanics. So some students are funny.

[00:02:08]They could look for a way of dodging some mechanics but now there is no option and the good thing is that the topics are a little reduced actually they extremely reduced when it comes to mechanics therefore the few topics which are left there is no way you can run away from them there's no way you can run away from them so that is why I chose to do resultant and motion remember those who were with us in the previous solid day we did connected particles resolving and yeah resolving and Newton's laws of motion that is motion of connected particles but so this now that was dynamics one so dynamics 2 is mainly motion without a force acting that is including things like projectile motion and resultant and relative motion though of the two it is resultant and relative motion which is a little more tricky. That is why you have chosen to begin with it when you're still more fresh.

[00:03:15]Okay. So, I've sent a PDF of this introduction on your own group. Hope you have seen it. And the password hope you have seen it also.

[00:03:25]So, resultant motion that's where I begin from. Resultant motion shall read step by step. Result motion consists of flying an aircraft. But don't worry, we shall not go through in the very details for us. What we want is something connected to velocity.

[00:03:42]So don't see this flying then you think we're going to go through very many details of pilots. No for us our interest is just something small something small the relative and resultant bit of it. Mhm. Then also steering a boat. So still even that no more no detail techniques but just that small bit of velocity that small bit of velocity is what we want. So resultant velocity is almost the same is okay the concepts are almost the same as resultant force by now I believe you know how to how to get resultant of a force. For example, they could say if a body two for act one going this side, okay, let me give it a little 5 Newton, another one going this side, let me say 2 Newton and they ask what is the resultant force and where will the body be moving? Of course, one should say that this one is bigger than this. Therefore, the resultant should be to the right.

[00:04:50]Meaning if this body must move to the right less than Newton's second law of motion. Okay, that applies to velocity still if velocity if here there is a velocity. I know you're wondering how it how can two velocities but don't worry we going to look at a scenario. So let me say one velocity is there another velocity is here. Let me say this is 2 m/s.

[00:05:17]2 m/s. This is 5 m/s.

[00:05:22]So the resultant of these two velocities is going to be to the right. Therefore this body the actual movement will be to the right. Though it will be small slower it will no longer be five because on this one this you must get a resultant velocity which by now we know that it's bigger by 5 - 2 which is 3.

[00:05:48]We are doing just subtraction because this is now called motion in one dimension.

[00:05:54]Motion in one dimension. If it was two dimension then we apply other techniques as we saw in resultant force. For example, when they give you this, one is this side, another one is this side.

[00:06:07]Maybe we shall see those details.

[00:06:12]But but I'll just use the basic that when there are two velocities on a body.

[00:06:19]Mhm. The resultant determines the actual direction of the body.

[00:06:27]With that, I'm going to give you a scenario. It is a funny one, but we're going to see if you believe it. But by by the end of the lesson, you have to believe it.

[00:06:37]So, let's first look at this video. It has some audio. So, let's first listen and see what it says.

[00:07:00]Uhhuh. That is something funny. Some students may fail to accept that is actually true, but I believe it is somehow true. Let me see those who can agree with me. Is it really true? Let me begin with Hannah. Hannah, are you there?

[00:07:16]You unmute and we discuss something.

[00:07:20]>> Yes, teacher. Uh, do you believe what the video said that when you throw an apple the other side, it again follows you?

[00:07:31]>> I could not hear.

[00:07:33]>> You can't You can't Okay. Uhhuh.

[00:07:36]>> Like the video has no sound.

[00:07:39]>> You couldn't? It has no sound.

[00:07:42]>> Yeah.

[00:07:44]>> What did I say? Okay, let me just see. I don't know what happened.

[00:07:58]How do they edit that?

[00:08:08]I don't know how to edit the sound now.

[00:08:15]Here it is.

[00:08:30]any I'm not sure. Did anyone Does anyone hear any sound?

[00:08:36]>> No, teacher.

[00:08:38]>> You can't.

[00:08:40]Okay, let me see if I can just use the actual video if you accept.

[00:08:52]I'm not sure how to do that.

[00:09:07]Is the sound now coming out? Oh, >> no.

[00:09:12]>> Not yet. Then I have nothing to do.

[00:09:15]Okay, let me just let me just explain something. So, this p this video is saying something. It says that when you are in a car and you're moving, then someone then you turn around. You saw how what has happened. Initially, it was like that. Then the man turned around. The one at the back, it moved and turned around. When he turned around, he threw an apple.

[00:09:49]The other side of the car is moving in opposite direction. He also throws the apple in the opposite direction.

[00:09:55]But the funny thing is that you see this apple is the I want you to analyze the motion of this apple. It is somehow funny.

[00:10:02]It's as if it is running towards the car yet it was thrown the other side. Let me first try to get Yeah, this man here is going to Okay, this man here turned around and threw an apple in this direction. Okay, but as the car was moving this up when it fell down, it began moving this direction.

[00:10:32]Now the question is is it really true or it is not okay anyone to give us something the audio I don't know I maybe by tomorrow I will have rectified how to get the audio but now I can't edit it.

[00:10:52]Yes, Stacey. Do you have anything to say?

[00:10:57]What made the apple go this side follow the car? Yet it was thrown towards this direction, but when it fell the ground, it began following the car.

[00:11:13]Oh, that is too much physics.

[00:11:15]Anyway, in math, we in math lessons.

[00:11:18]Mhm.

[00:11:20]Yes. Anyone with an idea of what really happened to make the apple go towards the car?

[00:11:34]>> Mhm.

[00:11:36]>> Um I think since it was in the car, it could be moving at the same velocity as the car.

[00:11:42]>> Mhm.

[00:11:45]>> Yeah.

[00:11:45]>> There are four Uh-huh. Then after what happened? I don't know.

[00:11:58]>> But you have an idea. So actually that is the truth. Let me first see because I've told you that it is possible for forces it is true. Someone can believe how a body can have more than one force.

[00:12:13]But when it comes to velocity, it is funny. For a body to have more than to have two velocities, that body must first be in a moving object. So this man here had an apple. So that apple when the when the car was moving this direction, the apple was also moving is also moving at the same velocity as she has told us. Now this man applied a certain pull through it this side with a certain velocity also. So in that case it means that there are now two velocities acting on the up one velocity is here with the velocity the car maybe the car is moving at 60 km/h.

[00:12:53]Mhm. Let's say moving like that. Then you throw it with a certain velocity but chances are high that this velocity of the car.

[00:13:03]It is not easy to throw this apple with a velocity bigger than the velocity of the car unless the car was moving very slowly. Unless the car was moving very slowly. So what happened is that this man threw an apple with a velocity smaller than that of the car. So let me say give an example. This is 60 and this is maybe 15 km.

[00:13:26]Maybe you throw your thing glass. You realize that there is something fun about the resultant.

[00:13:33]This resultant will be in the direction of the car. The resultant will be in the direction of the car. That is what makes the apple to move towards the car. So that concept is what we call resultant velocity.

[00:13:53]So resultant velocity in short the concept is close to is similar to resultant forces but this time we we're not using forces we are just using velocities.

[00:14:08]Okay if there's a question you can ask on the brief introduction but I'm going back to this to the slide one and we read through the notes.

[00:14:18]Um >> excuse me teacher. Okay.

[00:14:23]>> Uh, so you said that the car has its own velocity and then the >> man threw the >> the apple at its own velocity. So if say he had a slingshot or something like that and he was able to throw the apple at the same velocity at which the car is moving, would the apple stop moving?

[00:14:46]Would it just test still? Yeah, it will stay still and just fall. It is funny but you just fall down though it is not easy to believe but that is the reality.

[00:14:56]That is the reality because in resultant is the same as resultant forces.

[00:15:01]Okay. So this is what she was asking.

[00:15:03]She was saying that if this man was able to throw it with a velocity of 60 also maybe say 60 km/h and the car is also moving at a velocity of 60 kmh something funny would happen. this this thing would fall down would fall down would fall down okay hope I've answered you if there's any inquiry you can ask okay if no then we can first go back to the slide and we finish the words which were there okay so the pilot of an aircraft like I told In resultant according to our syllabus we we usually we deal with two main objects. We deal with pilot or we can say a car like that and a boat steering a boat. Remember steering is about water. Just a moment. Hello. Mhm.

[00:16:09]Yes. Good afternoon. Good morning.

[00:16:32]Y you Okay, I think we're now back online.

[00:17:05]Okay. So that's what I were saying like I was saying that here we deal with maybe pilot because pilot flying a flying an aircraft is affected by what we call wind by what we call wind. So that means that for you to fly an aircraft clearly to a destination you really want, you must also cater for the velocity of the wind at that time.

[00:17:29]Otherwise, it may affect your final destination. It may affect your final destination. And you are interested in linear velocity. We don't we don't say that you move in a circle. No, it is linear velocity. Of course, practically a an aircraft can make a a turn sular turn like that. But in this topic, we don't go in those details. We're interested in something linear. If I begin in this direction, I must proceed to that direction. If I'm to turn, I turn to a specific direction and move in that very direction. We don't go in details of a stop kind of velocity.

[00:18:12]Okay. So the two cases are for the aircraft and for the for the things like ship boat those things which are affected by the velocity of the river because we all know that rivers they keep the river keeps flowing so that mean that if I'm moving in a river and I don't care for the direction of flow of this river it means that I would be affected I may not reach where I'm supposed to reach and why Is it so? It is because these things they must be a resultant. There are two vices acting on that body. So because there are two vices acting on that body. The final direction will be the resultant final direction will be the resultant. That's why I began by showing you a video of someone throwing an apple this side. But the apple is in the couch is moving in velocity. So the actual direction of this apple must be the resultant of these two velocities. Same applies to the flying an aircraft. The actual direction where the aircraft will actually move must be the resultant of the two. We have what we call velocity of the velocity in still air. That velocity is the velocity with which the aircraft is set to move.

[00:19:33]Is set to move. Others call it initial velocity. It is okay set to move. But as it moves, there is another velocity which acts on that aircraft that is called velocity of the wind. Okay. Now combination of those two velocities will give what we call resultant velocity and that is what this topic is all about. We're interested in that resultant velocity. We're interested in that resultant velocity.

[00:20:02]The same explanation works for the boat or ship. The the boat is steered in a certain direction. That velocity with which you steer it we call it velocity in still water. So in most of the questions you'll be hearing saying that word velocity in still water. That means that the that means the velocity with which you set the ship to move or set the boat to move. But as it moves there is a velocity of the current that flowing water also affects also acts on this shape because there are two velocities we must get a resultant for us to know the actual path which the boat will take. So that is make a brief introduction about resultant velocity. If there's any line you have not understood, you can ask on this slide and explain it a little better.

[00:21:13]Yes. Is there anything you need to ask on this slide?

[00:21:19]Any line?

[00:21:35]Okay then.

[00:21:37]Okay. Elizabeth is the first slide.

[00:21:40]Okay. The write up.

[00:21:49]Are you there?

[00:21:50]>> Yes sir.

[00:21:52]>> Is the first is this side okay then? Muhaw Ayana is this slide okay?

[00:22:09]>> Yes.

[00:22:11]>> Okay that's good. Now we going to we want to look at the effect of that flowing current with a certain demonstration.

[00:22:19]With a certain demonstration we already seen that okay so when you're crossing a river like I've told you there's an effect of the flowing current. So that means that you need to know what you want. There are different case of of crossing in which you want to cross a river. Let's look at them. It says when one is to cross a river from one point of the bank to a point on the other bank a river is like this. So when you're standing here the shore that is called a bank even this other point. So one can want to cross from here to here directly. That is called crossing directly. Okay. Another one may say I want to cross and I reach here.

[00:23:09]They will tell you. Another one will say I want to cross and I reach here. Now this things of crossing a river there's a term we need to know. There's a a word called upstream and downstream. Upream and downream.

[00:23:27]What do they mean?

[00:23:30]Upstream and downstream. Let's say this very example. If the river is flowing this direction okay with a velocity and I'm here my boat okay person let's say person and I'm here because the river is running this direction this part here let me say this is region A region B region A is what we shall call upream so upstream depends on the flow of the river this part here where the river is this This part B is now what we call downream.

[00:24:07]That means that when I change and I do something different, let me say I have something here. I'm here. Then the river now is changes and goes this direction.

[00:24:17]Okay. Now that everything changes now, now this part A is what we call upream.

[00:24:25]Upstream. This part B is what we call downream.

[00:24:30]Like that. The reference point is this point where the where the person is who wants to cross the reference to that person. So these are the two key words we need to remember when you're dealing with questions of crossing a river.

[00:24:46]Mhm. Then this these lines are what we call banks. This one is one bank. This one is the other bank.

[00:24:55]Uhhuh. Let me say let's continue. The effect of current stroke river flow has to be taken into consideration and there are three ways in which one can cross a river. One I may say I want to cross the river by the shortest route. Shortest route. What does that mean? Shortest route. Shortest route means for me my aim is to cross the river. I don't mind where I should reach on the other side. For example, when I'm here, I I just want to cross and reach this other bank here. Anywhere along here as long as I've crossed, that's what we call crossing by the shortest route.

[00:25:40]Meaning that for you, you'll take direct motion like that. No, but because you because there is flow of current, this current will push you and make instead of reaching here, you'll end up reaching somewhere else.

[00:25:54]That is called crossing by the shortest route. You don't mind the exact location you want to reach. As long as you have crossed, that is all. That is all. Then we have what we call crossing in the quickest time. We going to a video that crossing in the quickest time. Crossing in the quickest time means you are here. You want to go here. Okay?

[00:26:21]Because of course of your distance. You want to go here. But you here you want to exactly reach you are at A and you want to exactly reach B. You must reach B and nowhere else. So what does that mean? In that case it means that you have to get for the river flow. meaning that you steer your boat in a funny way.

[00:26:41]We're going to say, but you see it going this side. It looks funny because someone may think that if I'm go this side, I'll reach somewhere here maybe, but that's not the case because there is a river pushing you this side. You steer going this side, but you end up reaching at point B.

[00:27:00]It looks as if it is not true, but it's actually true. It's actually true. So let us first see a video and you see what I'm talking about.

[00:27:15]There are three cases of this video.

[00:27:17]This one is called crossing in still water. Still water. Now this one is like it's a driven belt. But in this case I'm not going to drive it. I'm going to keep it stationally and I'll just release this car and you see what happens.

[00:27:32]This what has happened the river is not flowing. So it if you leave if you move in this direction you'll actually reach you'll actually reach. But what if the river flows that now that is what we call velocity in still water.

[00:27:50]Velocity in still water. But the river will never be ste will never be stiff and not moving. So we have to also cater for an option where the river is moving.

[00:28:05]So this is another scenario whereby the river is moving.

[00:28:11]Let's see it. You see what is happening to this belt. The belt is moving when I release it. I reach somewhere else. Not I intend to reach here. But I didn't reach there.

[00:28:24]When I released it, I thought by all means I would go up to here.

[00:28:30]But that is not the case. Why? Because this river is also flowing in certain direction. Let me play it and you see you're going to see that this car will not actually reach here. It's going to reach somewhere else.

[00:28:45]What has happened? It is reached somewhere else. So that is what we call crossing by the shortest route. You you don't mind where you're going to reach along the bank. As long as you cross, you have crossed. That is called crossing by the shortest route.

[00:29:05]So this is trying to show us what has happened.

[00:29:08]The person drove with this direction in this direction that is called now in our case it will be called velocity in still water. Is that boat?

[00:29:20]If it is an aircraft, I will call it velocity in still air. Mhm. But the boat you must have notic that it was moving this direction.

[00:29:30]Now these two velocities, the velocity of the boat of the river and the velocity of the boat must combine to get a resultant.

[00:29:41]So that resultant pushes the car somewhere else this side. That is why you didn't see it reaching this actual point.

[00:29:51]And in that case, we call it crossing in the quickest time. You don't mind where you land on the other side of the bank.

[00:30:00]You don't mind where you land on the other side of the bank. Hope you have taken note of that. Mhm. Let's look at this last option. Then I I'll allow you to ask when need be. Now here there is something I want to reach exactly here.

[00:30:20]So for me to be able to reach exactly here, I must for the flow of this river.

[00:30:26]How? By releasing my car in a certain direction this side. So the the river pushes me here. It looks funny, but you look at this demon. You see this? What has happened? This what is happening. I'm moving it this side, but it's actually going to land here. It's actually going to land here. Let's repeat again. You see?

[00:30:49]It has it is drifted this side but goes here. Why? Because we must be keen on what we call resultant velocity.

[00:31:02]Okay. So that was a long introduction but the question so far you can ask before I go to the calculations.

[00:31:15]If there's a question in the introduction, you can ask cuz now with that introduction, I believe we can be able to follow the calculations which you're going to do after.

[00:31:39]>> Mhm. Does the silence mean there is no question or does it mean? I have a question.

[00:31:46]>> Okay.

[00:31:48]>> So, I just wanted to confirm that you can cross using the shortest route. Um, either when the water is still or when you first start moving at a an angle, then the water the flow of the river takes you back to where you want to go.

[00:32:06]>> Now, in the questions we shall do, I think I gave you a first example where we this belt was on moving. Uh-huh. But because we know that a river can never be that still. It can never be that still. So that so those questions which involve when the river is not flowing at all will not be set. The ones should be set are the ones when the river is flowing with certain velocity. Same applies to the aircraft. The questions whereby the aircraft is flowing and there's no wind velocity will not be set. The ones can be said are those ones whereby the there must be a significant wind significant wind velocity because not all wind can push an aeroplane to move in a different direction but there's some kinds of wind which can I think you have seen those who watch some news you have seen some which are funny winds which can even uproot a tree those hurricans but we don't go in the details but in short what I wanted to answer is The questions whereby the river is not flowing at all are not exam will not be examinable. The ones are examinable when the river is flowing.

[00:33:19]I don't know is it better now?

[00:33:23]>> Um yes teacher and then okay lastly >> or the quickest time is that when you just let the river take you or you let the wind take you? Uh yeah, you let the wind take you to where as long as your your aim is to reach the other side of the bank. You don't mind which part you reach.

[00:33:44]You don't mind which part you reach.

[00:33:47]>> Okay. Thank you.

[00:33:49]>> You're welcome.

[00:33:51]Yes. Any is there any other inquiry?

[00:33:57]Su is there any inquiry?

[00:34:09]Okay, now that there's no inquiry, we can go to the items.

[00:34:20]Like I've told you, there are three categories. One Why you cross by the shortest route?

[00:34:29]Mhm. Let's try to see what it says. When one wishes when one wishes to cross the cross a river by the shortest route. So in in items we'll be doing you should look for these words. The words called shortest route. Shortest route. Another one you should do for is called shortest time or quickest time. Quickest. Let's use quickest or fastest time. Quicst time. Those are the ones which give you the how your diagram will look like diagram. Mhm. Now here they are saying when one wishes to cross a river by the shortest route Mhm. It implies that he intends to reach up at a point on the other bank directly opposite his starting point.

[00:35:29]Mhm. He must therefore set his boat upstream. Upstream is what I've told you. I think you saw the the car the toy car we used it was set to move in this direction. But along the way because this was moving the man ended up reaching here. That is what we call by the shortest route. Your intentions to reach the point directly opposite your starting point. If I'm here, I must reach here. If I'm here, I must reach here. Directly opposite. If I'm here, I must reach here. A point directly opposite. Remember that word. you when you're here and you want to move by the cross by the shortest route, you your intention is to reach a point which is directly opposite where you are on the other side of the bank.

[00:36:23]Mhm. Let's proceed. It imply intends to reach at a point on the other bank directly opposite his starting point.

[00:36:33]Okay. He must therefore set his boat upstream. Upstream. I've told you if I'm here and the river is moving this side then this part is what we call upream.

[00:36:47]This part is what we call downstream.

[00:36:49]Now if I move it downstream something funny I will have again destroyed everything. You see if I move it this side. Mhm. The river is also moving this side. I will have destroyed everything because it will just go this very far isn't. So for me to reach this side I must set it upream. So the river pushes me to where I actually want to reach.

[00:37:15]That's what this statement says. Mhm.

[00:37:19]Then this statement says the resultant velocity must be in the direction where intends. Do you see that word intends?

[00:37:28]Intends the where you intend to go is where your resultant must be. Mhm. We going to see the diagrams. Don't worry.

[00:37:36]But this is what we want. Where you intend to go. So if I'm drawing like this, I'm here. I intend to go here.

[00:37:43]This is this velocity here is called resultant.

[00:37:48]Velocity. That must be called resultant.

[00:37:51]Then the velocity with which you set the boat upstream is what we call velocity in still water. Still water. Then the velocity of this water is what we call velocity of current. current water or we can say the loss of water if the but current is the same as water somehow.

[00:38:13]Okay. So that mean that you if you want to reach here you must be calculative you must know what angle should I set my boat so that I reach here because not any angle will enable you reach here.

[00:38:28]Not any angle will enable you reach there. So this part is actually they want us to calculate what angle should I set my boat so that I reach the side which is directly opposite my starting point. That is what this first part is all about. Let us read this item and we see it says at lea in eastern Uganda.

[00:38:55]Okay. A group of senior for students are carrying out a field study on water transport and relative motion. Mhm.

[00:39:04]Don't worry this word don't worry it means but don't worry for now. During the activity, one student is asked to row a small boat from the southern bank.

[00:39:20]Mhm. Of a river directly to the northern bank. So if this is my compass, I'm here southern bank. Then I'm I draw it directly that word directly to the northern bank. That is means I must reach a point directly opposite my starting point.

[00:39:40]Mhm. Let's go the next paragraph. The river is flowing due east at a speed of 3 kilometers per hour. Okay.

[00:39:54]The student can row a boat the boat in still water. Do you see this word still water? Those are key words. At a speed of 5 kilometers per hour. Okay. Mhm. The teacher explains that if the student rose straight north, straight north means directly this. Mhm. The boat will drift eastwards. That is what I was telling you that if I'm here and I draw it and I set my boat northwards, the boat will not reach here. It will drift eastwards and go this side. So I I'll end up reaching this side. Okay. Mhm. Now, let's proceed with the paragraph.

[00:40:41]The boat will drift eastwards because of the current. Mhm. To reach the point directly opposite. Do you see that line?

[00:40:51]To reach the point directly opposite on the northern bank. Mhm. The student must ro in a certain direction which we don't know but we have to calculate it. Mhm.

[00:41:04]Hint. The river is 100 m wide. Now let's see the task.

[00:41:12]Determine the direction in which the student must draw in order to move straight across the river towards the north. Then Roman 2, calculate the time taken for the boat to cross the river.

[00:41:32]So you are here.

[00:41:34]Mhm. I want to reach directly opposite here. Now they're asking with which direction should you row so that this river pushes you this side and you reach where you intend to reach like that.

[00:41:53]Mhm. Let's draw a sketch diagram.

[00:41:58]Those are the two banks.

[00:42:00]The river is 100 m wide. So you can change it to kilometers. Why? Let us see the question. The question remember we have to use same units.

[00:42:12]Now here okay discard remember we have to use same units. But when you look at this question the velocity was in kilometers per hour and our distance was in meters. So that is something not okay with the units being they're not equal. This is in meters this is in kilometers. So is not okay.

[00:42:32]So you have to to change them to same unit.

[00:42:37]You either change these ones to become m/s.

[00:42:42]Mhm. Or you change this one to become kilometer. You change that one to become kilome. So for me I chose to change this one to become kilome. But either way is okay as long as the units are consistent.

[00:42:58]Okay. So this is where we were. We had drawn that.

[00:43:04]So this is what we I was saying. I want to reach where I intend to reach is where my resultant will be. The river is flowing this side. Because it's flowing this side. For me to reach here, my boat cannot go this side. That is not okay.

[00:43:19]It will just be pushed further away. So by all means, my boat must be in this direction. But I don't know the angle yet. So I have to use some mathematics to calculate that angle. So if I put the direction then from there I get the river like that. So this one is what we are going to get using some mathematics.

[00:43:45]Using some mathematics.

[00:43:48]Okay. I think someone already has an idea of how to get theta. Anyone to tell us from that diagram is it possible to get theta?

[00:44:06]Anyone li any idea on how to get theta?

[00:44:19]The good thing it is a right angle triangle.

[00:44:22]It is a right angle triangle. So can use so to get theta anyone bonji.

[00:44:43]Um maybe we can use co because we have adjust >> we have what >> the adjacent >> and hypotenuse the velocities >> the adjacent is what >> adjent is 3 km hour and then hypotenuse is 5 km hour.

[00:45:09]>> Okay that is true that's what you should do. So because there is a right angle triangle, we're not using any we're not using any we using it because there is a right angle triangle. If you don't notice a right angle triangle, then you can never use you must use cosine rule and s rule.

[00:45:33]But with this question, the good thing is it's a right right angle triangle. So I can just use that and say that when the angle's here, this one becomes opposite.

[00:45:43]Mhm. This one becomes adjacent and this one becomes hypotenuse.

[00:45:50]Therefore for me to get theta I will say adjacent over hypotenuse. And from adjacent over hypotenuse gives you co gives you cos. That means I can I can now get the angle with which I should steer the boat. So the boat must be steered at an angle of this to the bank.

[00:46:11]That is what we call direction. So basically that is Roman one. The question you ask Okay. So that means we can now proceed to Roman 2 if there's any question. So Roman 2 says they calculate the time taken for the boat to cross. Uhhuh. Now always now this is some they they look funny. You see I have this velocity.

[00:46:58]Okay. I already know that time time will always be if speed is constant time okay distance is equal to speed time time meaning that time will be distance over speed but the question is which of these three velocities should I use cuz I have this one velocity in still water. Mhm. I have this one velocity in steel velocity of of current. Mhm. I have this one which is called resultant.

[00:47:30]Now what do I use for you to get to for you to use this formula? The velocity must be resultant.

[00:47:39]The velocity must be resultant because this result means a combination of these two when I've joined them already.

[00:47:48]That's what resultant means. So always for you to use this formula of time equal to distance t = to distance over velocity this one must be resultant always resultant velocity. Mhm.

[00:48:08]And because we're using that resultant velocity the distance you use must be the distance moved along the resultant velocity. This one. So this D is called distance.

[00:48:21]You should write them somewhere.

[00:48:23]Distance along distance along resultant velocity. I want you to note it somewhere because some may be disturbed. Which distance are we going to use? Which velocity are we going to use? It is true there are three velocities but the resultant is what combines the other two which were acting on the boat. That is why we use the resultant and the distance we're going to use must be the distance along the resultant velocity along the resultant along the resultant. So that means that for me to get time I already know the distance along the resultant it is 0.1 kilome. Okay. But I don't know yet this V.

[00:49:09]Mhm. But the good thing this is a right angle triangle. Each time you notice a right angle triangle, it means that Pythagoras theory can work.

[00:49:21]Each time you notice a right angle triangle, it means Pythog theory can work. So let's try to use Pythagoras theory, we shall come up with that V as 4 km per hour.

[00:49:34]And when I have the velocity, when I have the resultant velocity, let's not just call it velocity. when I have the resultant velocity and the distance along the resultant and the distance along the resultant I can get the time taken not my words the velocity we use is called resultant velocity and the distance we use is called distance along the resultant that's why you saw me use AB here distance along the resultant. So that gives you the time taken.

[00:50:17]Okay. And this is a question you can ask on this item.

[00:50:24]Yes, Elizabeth.

[00:50:30]Elizabeth, you have a question.

[00:50:46]No, sorry. I don't have a question.

[00:50:48]>> Okay.

[00:50:54]Nana, is item one okay?

[00:50:59]>> Yes, it's fine.

[00:51:01]>> Okay, that's good. Mhm.

[00:51:17]teacher.

[00:51:18]>> Yes.

[00:51:20]>> I don't understand the concept behind the four like getting the roo<unk> of 5^ 2 - 3^ 2.

[00:51:28]Yeah, it is because okay some students that's where I would drop them from because some students know that for you to use a pythograph it must just be this maybe plus this. Mhm. Then you get this.

[00:51:41]No, before you use Pythagoras you have to first know which one is hypotenuse.

[00:51:48]Which one is hypotenuse? So my right angle triangle is like this. Meaning this one is called hypotenuse. So when I put C here and A it means that it is C which will be equal to A² + B² Mhm. But when I want to get B I cannot use B is not a hypotenuse because it is not I must make the subject I must make it the subject. Let's try C^²= A² + B 2. Now let me make B square the subject. I'll get c^ square 2 - a 2 put square root that's why I get c^² - a 2.

[00:52:30]So in short you don't you only put a plus here if what is here is a hypotenus. I don't know if I've answered you.

[00:52:40]>> Yes teacher you have. Okay, then let me first see.

[00:53:01]Yes, divine is item one. Okay.

[00:53:07]Yes, it is.

[00:53:09]>> Okay.

[00:53:11]Then I'm seeing two hers. I don't know who but okay. Let's me choose someone else.

[00:53:19]Precious is item one. Okay.

[00:53:24]>> Yes.

[00:53:26]>> Okay. Then we can now proceed to item two.

[00:53:43]Item two says during a weekend during a weekend sports training session, okay, at River Nile near Ginger, a group of students are learning about swimming safety, okay, and the effect of water current two points A and B are marked on the on opposite banks of the river such that A is directly opposite sorry B is directly opposite A. So if A is here, B should be here. Directly opposite.

[00:54:24]One student who is strong who is a strong swimmer is able to swim at a speed of this in still water. Know that word still water. However, the river is flowing downstream at a speed of this downstream.

[00:54:42]Mhm.

[00:54:44]The student wants to swim from point A to point B without being swept downstream. Do you see that word? Without being swept down.

[00:54:55]So I want to move from here to here, but I don't want to end up reaching this side downstream. I want to reach exactly here.

[00:55:03]Not that concept. Mhm. To achieve this he adjusts his swimming direction carefully. carefully means you must be mindful of the angle with which you start with. Mhm. So that his actual path is directly across the river along line AB.

[00:55:26]Okay.

[00:55:28]It is observed that the student takes 2 minutes to reach the opposite bank.

[00:55:34]Mhm. Task one. Determine the swimmer's speed along A. We're going to read the moment where AP is. Calculate the width of the river.

[00:55:47]Okay. So, one, we shall need to make a sketch. Velocity diagrams are drawn with a ruler. Like I told you here, we don't go in the details of a sketch of a case whereby the maybe the pilot or the ones in the boat changes direction. No, the one you begin with, we want to maintain it. We want to maintain that the case we deal with. This other complex case, we don't deal with it. That's so in short, use a ruler to draw a velocity diagram.

[00:56:24]Okay?

[00:56:26]So, I know that this is A, this is B.

[00:56:28]Like I've told you, where you intend to reach is where your resultant must be.

[00:56:36]Where you intend to reach is where your resultant must be. Then the velocity still air water depends on this direction because it is moving like this. I cannot take it this side. That is impossible. It will not enable me achieve what I want. So the only option I have is to take it this side. But the question is by which angle should I steer? By which angle do should I steer?

[00:57:04]That should be also be into consideration. So let me steer the boat.

[00:57:09]This side I've just made this one an improper fraction. I've just made an improper fraction.

[00:57:15]This one there's the velocity in still water. This angle is equal to this reason alternating angles. Okay.

[00:57:26]So from here it means that when I have this and I have this I can get V from Pythog theory and that will be the speed. Speed means magnitude of velocity and speed means you don't mind the direction. So this is now what we call speed along here. We don't mind the direction. So speed is that Now after that speed they want what we call the width. Width is this value of d. Mhm. But the good thing in the question they gave us the time and there's something relating those three resultant veloc resultant velocity distance along the resultant and time taken. Those three are connected that if t will be equal to distance along the resultant divide by resultant velocity.

[00:58:24]So when I have this and I have this which is here this is here it means I can get d which is this part width of the river like that. So let's try that.

[00:58:40]So that AB is equal to that whereby this is the resultant and this is the time but you have to change it to minutes because I told you the units must be consistent. If this is per second it means your time must be in seconds.

[00:58:59]Must be in seconds.

[00:59:02]Okay. Unless the question to ask on that you can ask Excuse me, teacher. I have a question.

[00:59:38]>> Okay.

[00:59:41]>> Um, when you were drawing the the line that has 25 over 18 m/s, >> how did you determine there's something you said about the direction of current that I didn't understand >> why you drew it this side and not this side. Okay, let me explain it. Now, this one direction of current shows you this is actually a river that I didn't put, we don't go into that finite, but a river and that river is flowing this direction. Now, when I'm here and I set it this side, this river will just push it further this side. So, I'll end up preaching somewhere very far downream. Yet in the question they said the the person must reach the opposite bank not away from the bank but just this point. So for me to reach there I must set it this side >> so that this river pushes me to where I want.

[01:00:42]>> Oh >> yeah.

[01:00:45]>> Thank you.

[01:00:46]>> You're welcome.

[01:00:52]Okay. If there's an inquiry, you ask.

[01:00:59]>> Um, excuse me, teacher.

[01:01:01]>> Yes.

[01:01:03]>> Could you explain how we got the wed >> there's a relationship between these three things? I think remember in item one we say that time taken is equal to distance along the resultant over velocity. This velocity must be resultant must be resultant. So for me what I did I made this d the subject. So when I make the subject I'm going to come up with t * v time * result time velocity.

[01:01:39]That is where this formula came from.

[01:01:42]This one.

[01:01:44]Is it better now?

[01:01:55]Yes. Don, is it better now?

[01:02:01]>> Yes.

[01:02:02]>> Okay. So, in short, yes.

[01:02:07]>> Mhm. Um so what's the difference between velocity and speed? Sometimes when we are given speed we use it as velocity.

[01:02:16]>> It is true all of them are the same. The only difference that if they ask for velocity for example in this question do you see this Roman one if here they had said velocity do you see that word velocity here after getting this value I must conclude by putting their direction. Which direction? here isn't I would say velocity velocity is 10 / 9 m/s in the direction in the direction along a like that. So this statement whereby you attach magnitude and direction is what makes it velocity because we know the difference between velocity and speed is that speed is called if I'm to use a more technical word speed is scalar and and velocity is vector. So speed you only mind the magnitude only.

[01:03:20]But when it comes to velocity you also cater for direction. So by me writing this word here direction this I have changed it from speed to velocity. I don't know if I've answered you.

[01:03:38]>> Yes teacher. Thank you.

[01:03:40]>> Okay.

[01:03:48]There's a question you ask.

[01:04:15]Yes. Any inquiry?

[01:04:53]So basically that is crossing by the shortest route. The this one let me see this one now what it says it says when one wishes to cross a river in the quickest time the co set will be directly across the river. Mhm. The current will then carry the boat downream somewhere else where we don't know where we don't know. Let's just I know it's about time but let's try to understand this part also. It says at River Nile a group of students are learning about the motion of boats in flow in flowing water. During a physics field study, a small mo motor boat is used to transport supplies from one side of the river to the other. Okay.

[01:05:50]The boat can move at a speed of 6 km/ hour in still water.

[01:05:56]However, Mhm. the river current flows downstream at a speed of 4 km per hour.

[01:06:04]Okay.

[01:06:05]The river is 250 m wide.

[01:06:11]The boat operator decides to steer the boat directly. You see this word? It changes a lot of things. The boat operator decides to steer the boat directly. So this is where your initial velocity will be. Now this one is no longer resultant is where you are steering the boat. Is why steering the boat. Let's proceed so that it reaches the opposite bank in the shortest possible time. As the boat crosses, the flowing water carries it downstream. So as it goes, the water will push it side. So you end up reaching somewhere else.

[01:06:50]Let's see the task. Calculate the shortest time taken by the boat to cross the river. Okay. Roman 2. Determine the distance downream by which the boat carries by which the boat is carried during the crossing. So distance downream is this one cuz we are here now we went this side and there.

[01:07:16]Okay, let's try to see it as we finalize one.

[01:07:24]We have seen that but we need a sketch.

[01:07:27]Those are the two banks.

[01:07:29]The width is 250 m. But remember, we want to make conent units. So I make it 0.25.

[01:07:38]Direction of the current. Mhm. Now this man does something funny. He p he sets his boat in this direction. Okay. Now because I set his boat in this direction, this current must push it elsewhere. it he will not actually reach here. He'll reach somewhere down as you saw there in one of the videos I showed you. So this what is happening this adds to this to give you a resultant somewhere else. So this man would end up preaching here end up preaching there.

[01:08:16]So this is what we call resultant. Now resultant is now this one. Hope you are not confusing the two things. Previously was here at Bris. That's where the man intended to reach but now here he's steering the boat in this direction. So the velocity in still water is this one.

[01:08:40]So make sure you understand the language used otherwise the diagram will be not okay. And when the diagram is not okay the working will also be not okay.

[01:08:51]So if there's a question on the diagram you can ask.

[01:09:00]So this is called resultant and this is called distance downstream distance down stream like that. This one is our rest in still water.

[01:09:22]Mhm. Then this one is our the rest of the current.

[01:09:28]This one is the direction to the bank.

[01:09:31]Direction to the bank of the resultant. Direction of the resultant direction of resultant.

[01:09:44]Okay. If there's a question on the diagram, I encourage you to ask because everything begins from a correct diagram. In mechanics, everything begins from a correct sketch diagram.

[01:10:03]Everything begins from a correct sketch diagram.

[01:10:12]Okay. So, So Tessy Abigail is the diagram. Okay.

[01:10:36]>> Yes teacher.

[01:10:40]So from the when the diagram is okay everything becomes easier everything becomes easier for example by similarity the thing was a right angle triangle I can use that so what where is the similarity similarity is coming from here do you see this triangle here and this bigger triangle here they all share a common angle meaning they are similar when they similar I can use similarity the one we're using that four over this this over this that is 10 okay will be equal to this over this which is d over 0.25 then I can make d the subject and that is all so when you use similarity you can get the distance downstream distance downstream which will be that Then they also ask for let me ask now here you see we doing we're adding there plus y let's go back to the diagram and we see in the diagram this v is now a hypotenuse that is why you are putting plus the v is now a hypotenus so they want distance downstream you have got it that was roman 2 then one the shortest Time taken. Shortest time.

[01:12:08]We said time is what? Distance along the resultant over resultant velocity. So now in this case our distance along the resultant is AB. If you look at it from here is our distance along the resultant. Then velocity velocity is this V. Now so that means that but in our question we only have this one. So you should look for a way of getting a B.

[01:12:37]You should look of getting a B either by Pythog or by whatever. If I want to use Pythagoras, I'll extract out this triangle. This one and I say this D I have got it already. This one is 0.25.

[01:12:54]So by Pythog I can get distance A.

[01:12:58]I can get distance A or I can use L. The good thing is a right angle triangle. So it is not that. So here I used Pythog theory and I was able to get the value they want. So when I get AB I can now remember the formula and substitute and get the answer.

[01:13:19]So basically that is item three. Give us the question you asked before we call it a lesson >> for the first part.

[01:13:32]Is there an issue with believing my answer is a fraction 1 / 6?

[01:13:38]>> No, in math it is okay.

[01:13:41]It is okay.

[01:13:46]Okay. Any other inquiry?

[01:13:54]Okay. Okay. So that means that I will I expect you to try some of the remaining questions and we tomorrow we shall see how you are fed in them. Otherwise have a good afternoon.