ZOOM LESSONS PART 5 | CLOSEST APPROACH | S6 MATH TERM 1 HOLIDAY | TUE 12TH MAY 2026 |

追加: 2026-05-15

[00:00:03]Yeah. So I was saying that we are proceeding with relative motion and now we on closest approach.

[00:00:10]So like we began from resultant velocity then we went to relative velocity then we went to displacement that is interception. Now in relative I think to remember that we said that VAB is equal to VA minus VB for this one interception means that the displacement apart is zero. So R A is equal to zero. Mhm. If it is not zero then we can get a minimum value. If it is not zero we can get a minimum value.

[00:00:52]That minimum value is what we call now closest distance of closest approach because I said some not much that always they will collide. For example, if you look here we said there is interception there they collide. Okay. But that's not the case always. They can just pass close to each other. They can just pass close to each other like that just close to each other. So they there will be a distance which is the smallest distance apart. Then after that they will get the distance will keep increasing. Look here the first the distance was getting close smaller and smaller and smaller but somewhere this where it reaches is not zero but keeps it smallest then keeps increasing increasing like that. So that means that that is called smallest distance of approach and that's what we want to calculate here. That's what we want to calculate here. There are different ways of calculating that distance.

[00:02:04]One if you remember the knowledge of calculus from causing calculus we know from turning point we know that we can get the minimum by differentiating. So if I differentiate I'll still get the answer. If I differentiate this ddt and equate to zero because you said for minimum you differentiate and equate to zero you still get the answer. Mhm.

[00:02:28]Another person can say because another person can say let me use completing squares. It is also okay because I think remember when you are still learning completing squares you could complete squares and get something like this maybe x + b² then plus something then you say that for minimum the whole of this is zero that also works but now for me I prefer a certain formula which I feel it is easier which I feel it is easier and that is the formula you're seeing on the screen so let's read and you see if two bodies do don't collide. Okay, there will be an instant at which they are closer to each other to each than they are at any other instant. So they keep coming nearer nearer and nearer then somewhere when this one's here this one's here meaning that they after that point they will keep the distance that will keep increasing increasing so that smallest distance is our interest that is what where the word closest approach comes in closest approach is subdivided into two parts one time and distance now is about assessment they can ask you for this time and distance for close approach.

[00:03:47]Here the best the easiest to me and what we shall learn in this video is vector approach. Using these two formulas they the only formulas you need to know but of course you have to know how this comes about because you already know in the previous lesson that A means R A minus R B provided this is a vector that is a condition it must be a vector. We also saw that VAB is equal to VA minus VB on condition that these are vectors.

[00:04:19]Then you also know R A B T I think you remember R A B T. How is it got? You get R A plus T V A B like that. So once you know that and remember these formulas you can easily get the distance and time for closest approach that's what we are going to learn today.

[00:04:43]Then the other part is co means okay in this in this part it means that they give you both the magnitude and direction of the two bodies. If we go here, it means that they'll give you this mag the magnitude of this maybe 30 km and also the direction maybe north.

[00:05:03]This one they also give you there speed maybe 50 km and the direction maybe north 30° east. When they do that it mean that what they want you to calculate is just closest approach and the time when they're close together.

[00:05:18]But if they give you one here they give you magnitude and direction and here they just give you magnitude. They can ask for which the direction in which this person should take in order to be as close as possible at some instant.

[00:05:33]That is where the word cost for close approach comes in. That's why the word cost for close approach comes in. They give you speed and they don't give you direction. Then they want you to calculate the direction.

[00:05:46]In that the better approach is geometry.

[00:05:50]Best approach is geometry.

[00:05:53]I believe by now you have tested a bit of vectors and a bit of geometry cuz I think remember and uh what for crossing a river we used geometry two diagrams then when it came to relative velocity we did both vector and geometry even yeah even yeah relative velocity for resultant we did only geometry so now for co approach the to me what is easier is when they ask for time and distance it is better use vector Okay. When they ask for direction, it is better use geometry. So those are the two parts we shall stick on. Those are two parts we shall stick on. But for today's video, we interested in seeing how these come about. If time allows, that's when we shall go to course. But if not, then course will be for the following day.

[00:06:47]Okay.

[00:06:49]So they said time for close approach is given by this magnitude. This one means magnitude. So you dot this is a dot it must be visible when you're quoting the formula. Make your dot visible. I don't know but I think you have done some part of vectors in math one and you must have done dot product but if you not yet we shall still I'll still tell you what it means. But this is dotting. Now you dot the initial relative displacement by the relative velocity then divide by the magnitude of relative velocity squared.

[00:07:26]Magnitude of relative velocity squared.

[00:07:28]When you do that what you get at the end will be called time for closest approach.

[00:07:36]Okay. When you get time, your work is to substitute that time here to get now the distance apart because we saw in the previous lesson that relative if I say a bt, it means relative displace relative displacement apart distance apart at any time t distance apart at any time t. So when you sub the time for close approach here, you'll get the distance apart at closest time like that. So as long if you can recall those formulas because they're not there in the log book. These formulas are not there in the log book.

[00:08:11]If you can recall them then the better the better. Okay. So with that we can now go through the questions. Actually that's the only introductory part on approach cuz by now you already know what RAB means, what VAB means, what RBT means. Unless the question you ask.

[00:08:33]Unless the question you ask.

[00:08:39]If not, those are the formulas. I encourage you to you can write them somewhere or you take a screenshot because they are the ones we're going to use always. Each time they ask for time, if you remember this, it is okay. Each time they ask for distance, if you remember this, it is okay. Like that.

[00:08:56]But like I've told you these are not the only methods like there are some teachers who prefer to use differentiation method why differentiate and equate to zero. It is a known concept because we know that when differentiate and equal to zero you either get maximum or minimum. So it is okay. Others will say let me stick to completing squares. It is okay. But from experience, some students make misfire when it comes to differentiation somewhere or some students miss when it comes to completing squares. That is why I personally prefer dotting cuz dotting is as we're going to see it is not that tasky. It is not that tasky.

[00:09:40]Mhm. Remember there is a vector symbol here meaning that if the question is given in terms of magnitude and direction you first convert it to vector as we shall see along the way as we shall see along the way. So with that we are good to begin.

[00:10:02]We are good to begin. Okay. So this one says it was a new paper but I just attached some scenario. So it says during a space motion simulation at Mccary University.

[00:10:19]Okay. Physics students are studying the motion of two particles moving in three-dimensional space with constant velocities.

[00:10:31]I don't know. I think I didn't send the PDF, but I'm going to send I'm going to send particle particle P moves with velocity this while particle 2 moves with velocity this when I when you see this when you see K it means it is now three dimensional but now here there's something funny from I you go to K meaning there's a J here which was not put but for you when you're writing you must put it there and say zero Okay, but best still it's better you write in column form so that you avoid the tasers I JK at the beginning of the observation particle P is located at a point with position vector this. Okay. And particle Q is located at the position vector this. Mhm. So that means that this one gives me RP. If you remember R means position vector. This one gives me R.

[00:11:35]This one gives me VP. This one gives me V. And that is all I need. If you look at if you remember the formulas we wrote that is all you need to once you have all those ones. Then you are good to go.

[00:11:48]You are good to go.

[00:11:52]So let's see. The students are required to analyze the relative motion of the two particles in order to determine when they come closest to each other. This word now is our keyword.

[00:12:07]Mhm. And how far apart they will be at that instant.

[00:12:14]Task determine the time at which the distance between P and Q is least. That is now t minimum.

[00:12:25]Mhm. Find the distance of particle P from the origin. Do you see that? From the origin means a position vector. So that is R P at that instant. R PT at time T. That means R P. Calculate the least distance between the particles P and Q. That is now R.

[00:12:49]Okay. R PT minimum like that. Okay.

[00:12:52]Let's go slowly. One, you need to remember that for from for time, you need to dot a b dot v a b. It is a formula which you need to do all you can to remember it. It's a formula. You need to do all you can to remember it like that. So I need to get ra and vab. Then I substitute in the formula. Let's do that.

[00:13:27]There's a zero there because the J was zero.

[00:13:31]So that means I can get V P2 like I've told you here they didn't specify this relative to this isn't so with even if someone does this it is okay someone does that it is okay but why did I choose V2? It is because using the concept I told you if I to get magnitude of this this 6 + 3 squar another one gets magnet of this 4 2 + 1 2 + 2 2 I think this will be bit bigger this is 64 + 36 this one is just 16 + 1 + 4 so this is smaller that is why personally I chose two ve of two relative to p but like I've told you it is just to make it more sensible. But if someone forgets and does this there is no loss of mark.

[00:14:25]There is no loss of mark. Okay.

[00:14:30]Then I also need to get the relative pos displacements I by subtracting. Now this after getting this and this I must quote the formula correctly.

[00:14:47]I must quote the formula correctly. The dot has to be visible.

[00:14:56]Some of you are funny. You just put a dot. You don't mind whether it is it has it is seen or not. No. In dot in vectors the dot has to be visible then we can substitute still here you see a dot must be visible. So how do we dot? Dotting is another way to is a way of multiplying vectors because vectors cannot be multiplied directly. You either dot or you cross. You either dot or cross. Now how do they dot? You say this time this plus this time this plus this time this.

[00:15:39]So in short after dotting what you are going to get is a scalar. Do you see here? Now there is nothing like a a vector. Now there's no I. Some students are funny. They want to put I J Kh that is now problems. Dotting two vectors will always give a scalar. So after dotting don't put I J and K. So 2 * 2 gave me 4 then plus -20 *1 gives me positive 20 then plus -8 * 5 gives me9.

[00:16:12]So that's where it came from. But remember there is a magnitude here.

[00:16:17]Magnitude means what is negative becomes positive.

[00:16:23]Magnitude means what is negative becomes positive. That's why you're saying here it was -66 but now it is positive. When you remove this magnitude sign like that even here this magnitude here you real here there's nothing like plus or minus it is just plus positive. So magnitude what is negative becomes positive.

[00:16:46]Here the formula you know for magnitude is must have square root. Okay. But here the good thing they put a square here.

[00:16:53]So what does that mean? It means that if you put a square root Mhm. that square root will go with a square to counter to cancel the effect. That is why you are not seeing any square root here on my denominator. It is because of this one that square there. Okay. And basically that is it. So in this topic once you quote the formula correctly there is no way you can okay you'll always get if you use a cash well once you quote the formula correctly what disturbs the students for getting the f the correct formula so I encourage you to look for all ways to recall that formula okay unless there's a question you ask on time the question you asked but mainly it is recalling the formula that is what disturbs many students recalling the formula once we get better of recording the formula. It will be good. You'll be good to go. You'll be good to go.

[00:18:25]So you must be also be king of the units. Do you see here? M squared, m/s and meters. So some students sometimes they can trick you. How? They can give you this in meters/s then they give you this in kilometers. Uh- uh then you don't hurry to substitute.

[00:18:42]You don't hurry to substitute. You must first change one of them. Either change the kilometers to meters to rhyme with this or you change the m/s to kilome/h to rhyme with this like that. So here they were okay because m so it is okay.

[00:18:59]And there the time will be in seconds like that. If this was kilome hour and this was kilometers, my time would have been in hours.

[00:19:08]The time would have been in hours.

[00:19:12]Okay, then we can conclude and that will be room part.

[00:19:24]So there's a question you ask >> excuse me teacher.

[00:19:38]>> Mhm.

[00:19:41]>> Um so when we finding the time >> I'm saying here we noted we denoted time with minutes and then we got our answer in seconds. So since we were working with m/s and meters, doesn't that mean that up here we have to write t with seconds not minutes? This one first way this 18 minutes. Okay, actually this one is a brief word to mean minimum. I don't know what you can use. Okay, you can use list to avoid confusion.

[00:20:11]>> I think mean will disturb you. Let's use list to mean list distance.

[00:20:17]It doesn't mean minutes. It means smallest. Okay. But let's change it to mean list to make it list. I think that will be better. That means even here the >> dim mean becomes now list like that.

[00:20:40]It is okay. It is okay. Now this will become list.

[00:20:46]list.

[00:20:50]Mhm. Then this will become list.

[00:21:12]Okay, I think that is it.

[00:21:16]Let me also yeah this is a question you ask on the time but usually like I've told you what disturbs is the recalling the correct formula recalling the correct formula is what disturbs.

[00:21:35]So after getting time you go back you can now get arity now and we know that R 2 P t will be equal to R 2 P + T V 2 P like that but our time is 2.2. So it will become now r 2 p in brackets 2.2 will be equal to what will be equal to this one which is 2 -20 -8 plus t which is 2.2 2 then plus V this one which is 21 5 like that when you are with the cash work it mean that you they must the answers will always come out when you're keen with cash work the answers will always come out. So let's try to expand that to get the distance.

[00:22:47]Substitute for t you come up with this. But remember the question was about distance and distance is scala question was about distance not displacement. Hey maybe hey this was Roman part was just position vector I think let part is okay they didn't ask for hey they said distance yeah distance of the particle from the origin okay then it is true you have to get the magnitude yeah and that is all for part B Yeah, if there's a question you ask.

[00:23:37]But we're now using the formulas we we have been using in the previous lessons.

[00:24:23]Okay, that was part B. Then part D. Now they want the relative displacement.

[00:24:29]So I sub code the formula correctly.

[00:24:31]Substitute for the time and that is all. But because they wanted distance, they wanted distance. So you go back to get the magnitude.

[00:24:44]You get the magnitude and that will be all.

[00:24:52]So basically that is clos approach not so complicated. It needs you to recall the other two formulas. The formula for time especially needs you to recall the two formulas. The formula for time especially the formula for time especially.

[00:25:11]When you call it correctly you're good to go.

[00:25:51]Okay, there's no question. We can now proceed.

[00:25:55]But let me first double check.

[00:26:00]Double check. Double check.

[00:26:04]This is item one. Okay.

[00:26:11]>> Yes teacher.

[00:26:15]>> Then we shall go to Jenny Nalima.

[00:26:25]Is item one okay?

[00:26:29]>> Yes teacher.

[00:26:30]>> Okay. So I'm going to send the items on the group. I just didn't remember that I had sent.

[00:26:40]So we shall now this one is still the same thing but we can see they want okay we can just go through it for confidence. But now what I want is what if they don't give you the the question in vector form what do you do? You have to first resolve. But let's first do this one again for just understand grasping during a three-dimensional motion experiment at Chamogo University. Okay. Physics students are studying the relative motion of two particles moving with constant velocities in space.

[00:27:23]Particle P moves the constant velocity of this and at a certain instant it passes through a point whose portion vector is this. What I want what should be I think there are no units. There are no units.

[00:27:39]At the same instant particle two passes through the point whose position vector is this while moving the constant speed of that. So they have given us all we want cuz what we want is relative positions and velocities. This one is for VP. This one is RP.

[00:27:59]This one is this one's position vector now. Yeah.

[00:28:06]Position vector RP. Then this one is V P like that. Mhm. So that mean we have everything we need. We have everything we need. So I can proceed.

[00:28:22]Determine the position and velocity of Q relative to P. Now here they will specify the order when you interchange it is no longer okay.

[00:28:33]You remember in the first part they didn't give us anything like this isn't.

[00:28:37]So if someone does this another one does this they're all okay. But now here in this question they have specified the order they want. They want two relative to in that case a student who does this is now off track.

[00:28:58]In that case a student who gets this will now be off track.

[00:29:05]Okay, that is it.

[00:29:11]So VP RP then we can now expand what RP is is R2 - RP subtract 1 - 6 -5 -2 - -1 9 5 - 4 1 like that there no units so don't put units no units same applies to relative velocity See no seal. Then next is I think that's what they wanted in Roman one.

[00:29:48]See there some buttons I didn't put first put Okay, I'm still will find something.

[00:31:32]Yeah, to go now.

[00:31:42]Just one more figure.

[00:31:52]Okay, now we're good to go.

[00:31:55]There was item two.

[00:32:02]So yeah, now what this is is quoting the formula correctly. Once you're able to quote it correctly, the rest becomes easier. So quote the formula for list time. This you have agreed you call it list it is okay min doesn't mean minutes it means minimum but if you sub call it list substitute for this also get the magnitude for this which is this and dotting after dotting you don't get any i j k don't put any i jk don't put any i jk then you realize that this one now when I sub when I do this addition I'm going to get negative for example -5 + 9 is4 but pos4 - 4 is -1 but because there was a magnitude here it means what is negative becomes positive so we're now seeing a positive 11 not negative reason we had put a magnitude sign we had put a magnitude sign also be keen there are no units on time reason in the in the given information there were no units so Don't put it mean that you should be consistent by not putting units like that.

[00:33:21]And is the question you ask?

[00:33:56]Then with this who can give us the leave us the next item. Yeah. Shortest distance. I want someone to take us through how to capture the shortest distance.

[00:34:19]anyone to take us through after getting the Cynthia, is this I'm not understand what the what you're marking on the screen.

[00:34:56]Cynthia maybe can explain what you're marking.

[00:35:22]Yes. So I want someone take us through how to get this shortest distance.

[00:35:26]Nisha, you can take us through Nisha. Are you there?

[00:36:00]Anyone?

[00:36:12]Nadong Bonji, you can take us through.

[00:36:21]>> Teacher, >> you want to get the shortest distance.

[00:36:25]After getting the shortest time taken time taken, how what should we do?

[00:36:45]I'm not sure what to do here.

[00:36:47]>> Mhm. Okay.

[00:36:55]Nice gift. Nice job. You can take us through.

[00:37:07]>> I think the time for the shortest distance.

[00:37:11]>> Pardon?

[00:37:12]>> We are going to the for have the time for the shortest distance.

[00:37:17]>> Okay.

[00:37:19]>> We're going to subitute into the formula. Give us the formula.

[00:37:32]>> Mhm.

[00:37:32]>> Give you back. The formula is first. I'm not getting to P. Mhm.

[00:37:52]into that time >> inside the into that time. Yes.

[00:37:59]>> Mhm.

[00:37:59]>> See will be equals to >> Mhm.

[00:38:04]>> the relative distance.

[00:38:07]Okay. QRP >> that is called >> that is called initial relative displacement. Initial relative displacement. Uhhuh. Plus what?

[00:38:20]the time.

[00:38:22]>> Yeah. The time which is 0.0ative 050 >> then relative velocity which is one that okay so you have a calculator we need to get what we get at the end to four decimal This >> gift was still there.

[00:39:02]I didn't hear what you said.

[00:39:03]>> I was saying with now use a calculator.

[00:39:06]What do we get when we add So, I wanted you to press the caption and tell us in short we add component by component.

[00:39:40]for the I Mhm.

[00:39:41]>> Yeah.

[00:39:43]We get um 4.9515 >> 95 >> 4.9515.

[00:39:57]>> Okay. Then we go to the J.

[00:40:02]I think it is.

[00:40:06]Mhm.

[00:40:09]9.0485.

[00:40:14]>> Then for K We get 0.275.

[00:40:47]>> We get what?

[00:40:51]>> 2725.

[00:40:53]>> Zero.

[00:40:54]>> Zero.

[00:40:55]>> Mhm.

[00:40:57]>> 2725.

[00:41:00]>> Okay, that's good. Try. That's good.

[00:41:04]negative.

[00:41:06]Okay, let me just double check. That should be correct.

[00:41:13]P is that then substitute.

[00:41:16]Yeah, mine is is it negative? Let me first double check with I'm getting positive but I don't know.

[00:41:28]Let me just try to see.

[00:41:32]M >> but it's not negative.

[00:41:35]>> It is positive.

[00:41:38]Okay.

[00:41:38]>> It's positive.

[00:41:40]>> Okay, then that's better.

[00:41:43]So, basically that's how they do questions of shortest approach. They're not that difficult, but you you must look for a way of recalling the formula.

[00:41:54]They're not that difficult, but you must look for recalling the formula and I think will be better.

[00:42:04]If there's a question you ask.

[00:42:22]So there are no units in the question.

[00:42:24]You don't put units in the answer.

[00:42:27]Yes. Hannah, you have a question.

[00:42:30]Yes, I have a question.

[00:42:33]>> Okay.

[00:42:34]>> Um, beginning at the beginning you gave us a formula for D minimum or D.

[00:42:43]>> Mhm.

[00:42:45]>> Yes.

[00:42:49]Yeah. I gave you you want to have a look at it.

[00:42:53]>> Pardon?

[00:42:54]>> No. I saying can we use that formula to get the D minimum? Yeah, the one you have used is only that because here you got time. Now that for means you the time you get here is what you substitute here in this bracket. You see that is why you seeing us in this room question.

[00:43:15]This t we have got here this value is what you're going to substitute here. Do you see it here?

[00:43:24]That's what the formula says.

[00:43:27]So in short you have used the same formula.

[00:43:32]>> Yeah we use the same formula.

[00:43:38]>> Okay. Okay. If there's any inquiry you ask.

[00:44:06]Okay. Okay. So that means we are good to this vector I want where you must get let me first this one.

[00:44:19]Yeah this is better to do this better to do.

[00:44:24]So the first two questions you have done the questions were in vector form I JK but what if they don't give you in vector form? What do you do? You must first look for changing them to vector.

[00:44:38]Now let's look at this item. It says at 10:00 a.m.

[00:44:45]during maritime surveillance exercise on Lake Victoria, two ships A and B are being tracked by a navigation control center. Okay. At that moment, the ships are 16 km apart.

[00:45:04]The distance AB is 16 km apart. Mhm. With ship A located on a bear ring of this north 35° east.

[00:45:19]So you should come and first locate that north going towards east 35. So that means that if this is 35 the side B is not that from A is let me see A is on a bearing of this from B meaning B is the one which is here and A will be here like that that why we doing that is to help us get the relative position relative position you can say relative position of A relative to B. So distance tense is about relative position.

[00:45:55]Velocity is about relative velocity like that.

[00:45:59]Mhm. Let's proceed. Ship A is traveling at a speed of 14 km/ hour on a bearing of south 29° east. So when you come here, south is here. East it is here. So this is 29 like that. Mhm. So that is the 14 for B.

[00:46:23]For B. Is it B? Let me see. For A. This is for A. Let's proceed. While ship B is moving at 17 km hour on a bearing of north 50° east. North is here.

[00:46:40]Northeast like this. So this is the 50.

[00:46:46]that is now B like that. So why do why do we do these sketches is to help us to change to vector. Vector means you resolve horizontally and vertically.

[00:47:00]Vectors means you resolve horizontally and vertical whereby the horizontal is up vertical is one below like that.

[00:47:08]Horizontal is the I and vertical is the J. That is the only new thing we're going to include. Then after that you go back to the formulas the two formulas we learned the one for T and the one for D like that. Okay. Now let's see how to do that. Now here they are specified in the question. It must be B relative to A.

[00:47:33]B relative to A. Meaning if someone does VA relative to B it is now off track. It is now outside what is required outside requirement.

[00:47:47]So you must be keen when they specify stick to it. When they don't specify it is you to choose though for me I prefer you look for the one with the highest magnitude like that.

[00:47:59]Okay. So let's see how to do such a question. one make some simple sketches which can help you to convert from magnitude and direction to vector that was VA it was south 29° east so it gives you that the reason why I'm getting this angle is to easily resolve because I think by now you know that it is easier to resolve if you have an angle to the horizontal easier to resolve when you have an angle to the horizontal Okay. Now the question is who can help me to who can resolve this one to the horizontal to the vertical?

[00:48:40]Anyone to give me VA in vector form in short? How to resolve?

[00:48:53]Mhm. Elizabeth Muka, you can resolve for us.

[00:49:00]We want to resolve this 14 to the horizontal and to the vertical. What do we write?

[00:49:17]I'm seeing your hand. Okay. Hannah.

[00:49:23]Mhm. What I got right >> 14 61.

[00:49:32]>> Mhm.

[00:49:35]>> Then for the 14.

[00:49:47]Mhm.

[00:49:55]Yes, you're still there.

[00:49:59]>> Yes, teacher. I'm still here.

[00:50:01]>> Mhm.

[00:50:06]>> It is 14.

[00:50:07]>> Then that's it.

[00:50:10]>> Oh, it's 14 sin 61. 14 sin 61.

[00:50:16]>> Okay. Is that all? We put units.

[00:50:20]Is there anything missing about negative and positive? Oh, it is okay.

[00:50:26]>> Oh, there's a negative missing on 14 sin 161.

[00:50:32]>> Yeah. So, that is >> 141.

[00:50:36]>> Okay, that's what I wanted to hear. So, to change in vector form, you must be keen on sign convention.

[00:50:43]To change from magnitude direction to vector form, you must be keen on sign convention.

[00:50:51]Okay, that was for VA. Also do we going to do the same for VB. Now I want another person apart from the one who has explained the VA to tell us how to get the VB in vector form.

[00:51:07]Anyone else apart from Hannah?

[00:51:19]Yeah, I'm seeing. Okay. Nadong, >> what shall we write?

[00:51:25]>> Um, four 17 >> 17 cos 40.

[00:51:36]>> Mhm.

[00:51:39]>> And then 17 sin 40.

[00:51:45]Is that all? Or there's any negative and positive missing?

[00:51:51]>> Positive.

[00:51:53]>> They're all positive.

[00:51:55]Okay, that is true. That is true. Okay.

[00:51:58]Mhm. That is it.

[00:52:02]So that mean that I can now get the relative velocity which was in part A.

[00:52:06]This one is here and this one came from here which you rubbed off. Then you can get the answer they want.

[00:52:19]Then let me see if they ask for magnitude how the test goes. Determine the velocity of ship B relative to A.

[00:52:26]Mhm. Now here like I've already told you you you specify direction in based on the question. Previously in the first two items the question was in I JK meaning the velocity if they ask for velocity you also leave your answer in I JK like that. But now here in this question the velocity was given in terms of magnitude and direction.

[00:52:54]This here you see this in terms of magnitude and direction of bearing. Okay magnitude and direction. So that means that even you your final answer because velocity is a vector quantity. They don't need to tell you to get direction you have to get it. Because velocity is a vector quantity they don't have to tell you. You have to get it. So get magnitude and also get direction.

[00:53:24]Direction depends on this positive horizontal to the right. Positive vertical upward. Then from start to end gives you relative velocity.

[00:53:40]But because they want the answer in terms of compass that is why you're saying me getting this angle from north because compass direction you either start from north or from south.

[00:53:50]So here you you cannot start from south because the angle will be bigger than 90.

[00:53:56]Therefore the only option is start from north going this side. That's why you see me putting the angle here. Then by geometry this angle can come here.

[00:54:04]Reason alternating angles.

[00:54:08]Then when it comes here and this is right angle. This symbol has to be there. Must it is a must. You must put this symbol for you to be able to use so when I'm here this becomes my opposite and this becomes my adjacent. So opposite over adjacent gives you 10.

[00:54:33]Then I can state the direction they want magnitude direction and that would be a complete answer. So velocity is a vector quantity. It must have magnitude and direction.

[00:54:52]Okay. If there's a question you ask, the only new thing we added is how to convert from magnitude direction to vector. Then from there we shall now that we have those in vector form, we can proceed to get the time and the distance.

[00:55:12]Okay. But so far there's any if there's a question you So when they went time we shall need to get this.

[00:56:07]So what you have not yet got so far is this error AB the VAB is here in vector form. Okay. VBA should now be VBA. Okay.

[00:56:16]R B A dot VBA BA over VBA BA magnitude squared magnitude. So we already have the VBA in vector form but we don't have this yet. So what do we do? We go back here and get the sketch which we are supposed to use. Here R B A means where is B located basing on A? When I'm when I'm at A, where is B located?

[00:56:59]When at A? Mhm. Where is B? That's what it means. A being A is the observer. B is what is being observed. So A B A means when you stand at A where will B be where will be B be?

[00:57:19]So go back to the initial position they said 16 km apart and ship A is located on the bearing of north 35° east 35 and this is 16 km. Okay. and they said A is here and B is here.

[00:57:43]So Arab AA means when I'm standing at A where is B? Where is B? So in short I have something like this. In short I have this I have B here. I have A here. This angle here is the same as this 35. But we need to get an angle to the horizontal which is it will be what is it 55 probably 55 this is 16 kilome so that means that when I'm standing at a to reach b it will be negative horizontal negative vertical if I'm to resolve so that means that should be r you can come and say a b a is 16 16 cos 55 and also 16 sin 55.

[00:58:43]There I've got RA in vector form. That's what RA means. R A when I'm at A, where is B? When I'm at A, where is B? So, let's do that and we see.

[00:59:22]So ara it means you are here you're trying to locate B. So move negative here and move negative down. That's why you see negative this negative this to give you this as your relative displacement in vector form. Now that I have BA and VBA, next thing is to remember a correct formula.

[00:59:48]Remember a correct formula. Then you can substitute. You must be keen on the decimals. Use four. Use four. Use four.

[00:59:57]Others prefer to use more than four. It is okay. But the more the decimal places, the more chances are that you may skip a certain digit. That's why we prefer four. And that is okay.

[01:00:10]Now here I already I had already got VBA. That is why I'm not repeating it.

[01:00:14]We're just saying VBA squared because I had already got it here in Roman in the previous Roman here.

[01:00:24]I already got VBA.

[01:00:29]Then I can use a calculator. Now this times this gives what? Gives this. Okay.

[01:00:35]Plus this times this gives what?

[01:00:39]Remember the magnitude side. So magnify means the whole of this will now become positive.

[01:00:45]Divide by this you'll come up with these hours.

[01:00:49]Then you can change to minutes.

[01:00:51]It is okay.

[01:00:56]Okay. Okay. If there's a question on Roman B Roman 1, I encourage you to ask Okay, then we can now proceed to Roman to this Roman 2.

[01:02:34]When you get time, you can now substitute here and use the cash correctly. You'll be able to get this. But that is still displacement.

[01:02:47]That is still displacement. So you have to get the magnitude still because the question talked about closest distance a scalar distance is a scalar.

[01:03:08]So once we get the magnitude then you're good to go.

[01:03:14]And is the question you ask?

[01:03:22]>> Excuse me teacher.

[01:03:24]>> Okay.

[01:03:26]On the first the part before I'm not understanding where the 16 kilometers came from >> on you mean this or >> yes >> 16 it was a it was in the question somewhere. Let me see. It was in the question somewhere.

[01:03:49]It was somewhere here.

[01:03:52]They said at that moment the ships are 16 km apart.

[01:03:59]So it was in the question.

[01:04:02]What is better now?

[01:04:06]>> Yes. Thank you. Okay.

[01:04:36]I still remind those with end of term passers to inbox me those papers cuz tomorrow we shall have we shall finalize with the last part of this relative motion and the topic will be done then you can think of what to do next.

[01:04:52]So I encourage you if you have the pass you send them so I can see if they can be they can benefit the rest.

[01:05:25]Okay. So now we can finalize by getting the magnitude then the time in clock time because I think the time was given in clock time.

[01:05:40]You should look at the question. Let's first go about the question and see here in the question they began by giving us the time in clock time here.

[01:05:55]Do you see that one? It means that even your final answer of time should be in clock time. That is why you're seeing me concluding with a clock time at the end of it all here.

[01:06:13]At the end of it all, I'm concluding with a clock time like that.

[01:06:19]Okay. Otherwise, I think we can call it a lesson as the question to ask.

[01:06:26]So, tomorrow we are concluding with geometry approach in when they ask for course for closest approach. when there for course for closest approach okay otherwise we can call a day I'll send the PDF on group