1 00:00:00,550 --> 00:00:10,210 So from your origin of a year, we define or a which is our position vector for A as this vector or 2 00:00:10,210 --> 00:00:13,670 B as that vector and then may have a relative position. 3 00:00:13,690 --> 00:00:20,320 So what is the position of a relative to be that would be this or a relative to be? 4 00:00:20,650 --> 00:00:27,370 And if you swapped that arrow around and you put it aside, it would be the position of B relative to 5 00:00:27,370 --> 00:00:27,760 a.. 6 00:00:28,180 --> 00:00:30,220 Now, the nice thing is we can. 7 00:00:31,690 --> 00:00:37,510 We can handle this as vector addition, so we've got these vectors and we can add them, we can say 8 00:00:38,050 --> 00:00:41,920 this vector is that vector, plus that vector. 9 00:00:42,190 --> 00:00:56,230 So meaning we can say that our position of eight is or B plus or A relative to be sort of Duniya, as 10 00:00:56,230 --> 00:01:02,600 I've said, that one is that one plus that one just the way you would normally add vector. 11 00:01:03,490 --> 00:01:13,110 OK, and we can therefore also say that if you differentiate this, we can say the early is the B plus 12 00:01:13,120 --> 00:01:19,360 the A relative to B, and these are all vectors. 13 00:01:19,390 --> 00:01:25,480 That's why they've got a little stripe, you know, so they're going to have iron J components because 14 00:01:25,480 --> 00:01:27,100 we just work in a two dimensional case. 15 00:01:27,100 --> 00:01:33,880 If we got in a three dimensional case, it would have had I, j and K components that we just going 16 00:01:33,880 --> 00:01:37,330 to have Einziger components adding these vectors together. 17 00:01:37,670 --> 00:01:39,820 And the same for acceleration. 18 00:01:40,300 --> 00:01:49,270 Acceleration of particle A is the acceleration of particle B plus the acceleration of particle A relative 19 00:01:49,270 --> 00:01:54,100 to B, and we'll do an example of that to show you how it works. 20 00:01:56,020 --> 00:01:57,640 So let's consider this example. 21 00:01:57,640 --> 00:02:01,720 I've done my best to try to do it properly. 22 00:02:01,720 --> 00:02:04,690 But what you have here is imagine two boats. 23 00:02:04,870 --> 00:02:08,380 There's Boat B in this boat and watching them from the top. 24 00:02:09,640 --> 00:02:10,850 This is a shoreline. 25 00:02:12,370 --> 00:02:13,740 So let's you have a beach there. 26 00:02:13,750 --> 00:02:15,790 This is a sea or a lake. 27 00:02:16,150 --> 00:02:18,370 And this boat is travelling in this direction. 28 00:02:18,370 --> 00:02:19,120 But B. 29 00:02:20,340 --> 00:02:25,920 And this boat, but I was traveling in that direction, it has a velocity of 10 meters per second and 30 00:02:25,920 --> 00:02:28,540 but because of velocity of 15 meters per second. 31 00:02:28,860 --> 00:02:31,740 Now note that these velocities are scalars. 32 00:02:32,730 --> 00:02:39,330 In this case, they they don't include the direction yet that just in this direction in which the boat 33 00:02:39,330 --> 00:02:42,400 moves, just going in that direction indicated by that arrow. 34 00:02:42,690 --> 00:02:43,540 Same with this one. 35 00:02:43,770 --> 00:02:48,270 So we need to break up this velocity into its components. 36 00:02:48,270 --> 00:02:54,420 And luckily we have a angle here and we have an angle there to do it so we can break it down into a 37 00:02:54,420 --> 00:03:00,950 component in the other direction and a component in the direction. 38 00:03:02,640 --> 00:03:08,520 And then we can add those components because what we want to know is what is the velocity of about a 39 00:03:08,520 --> 00:03:11,540 relative to both be OK? 40 00:03:11,910 --> 00:03:22,860 And we know that that would be we know that this has a certain formula and that that would be the miners 41 00:03:22,860 --> 00:03:23,700 will be on. 42 00:03:23,830 --> 00:03:29,960 So that would be the A minus the B, but these all vectors. 43 00:03:30,000 --> 00:03:33,920 So we first need to break this down into different components. 44 00:03:34,110 --> 00:03:35,040 So let's have a look. 45 00:03:36,690 --> 00:03:43,740 So what I've done is I've drawn a vector diagram of the movement of these votes like this. 46 00:03:49,150 --> 00:03:56,350 So, yeah, you have and they have to be this victor of a year indicates the velocity of Bird B and 47 00:03:56,350 --> 00:04:02,590 this one the velocity of but A, you can see that this vector is longer than this one because we have 48 00:04:02,590 --> 00:04:06,670 velocity of 15 meters per second versus a velocity of 10 meters per second. 49 00:04:06,680 --> 00:04:13,750 So this one is longer because the length indicates the magnitude of the velocity and then of course, 50 00:04:14,080 --> 00:04:15,940 the arrow indicates the direction. 51 00:04:16,630 --> 00:04:24,820 OK, so what we want to know is V of a relative to be so we need to know this vector of a year so we 52 00:04:24,820 --> 00:04:30,580 can get this vector of a year by just adding vectors. 53 00:04:30,580 --> 00:04:36,610 Or what we could do is we can use the cosine route because we just want the length of this and we can 54 00:04:36,610 --> 00:04:39,260 get the angle also with a room. 55 00:04:39,790 --> 00:04:48,580 So what the Cassandre says is that this length squared of the year is this is this length squared, 56 00:04:48,820 --> 00:04:56,980 plus battling squared minus two, this one times that one cosine of the angle between the two. 57 00:04:57,820 --> 00:05:06,250 So what it basically says is that the a relative to be so that's one of the squared 58 00:05:08,950 --> 00:05:12,670 will be this one squared plus that one squared. 59 00:05:12,700 --> 00:05:14,110 So we have that already. 60 00:05:14,150 --> 00:05:22,450 I was going to say ten squared, plus fifteen squared, minus two this one times that one. 61 00:05:22,480 --> 00:05:25,650 So it's going to be ten multiplied by 15. 62 00:05:26,260 --> 00:05:31,260 OK, and then we have the cosine of this angle between the two. 63 00:05:31,270 --> 00:05:32,930 So we know that angle is 30. 64 00:05:33,430 --> 00:05:34,730 This is 45. 65 00:05:35,230 --> 00:05:36,450 This one is 90. 66 00:05:36,460 --> 00:05:38,310 So that must be 45. 67 00:05:38,950 --> 00:05:41,640 OK, so this whole angle is seventy five. 68 00:05:42,220 --> 00:05:43,170 Seventy five. 69 00:05:43,930 --> 00:05:51,760 And so if we calculate this and we take the square root of that, we did the a relative to be. 70 00:05:53,600 --> 00:05:56,420 Is equal to 15, comma seven. 71 00:05:58,560 --> 00:05:59,720 Meters per second. 72 00:06:02,890 --> 00:06:07,850 So that is the length of this vector we don't yet know the direction. 73 00:06:09,100 --> 00:06:15,550 So let us find the direction if we define the direction of this vector with regards to the horizontal. 74 00:06:15,580 --> 00:06:17,370 We basically want that angle there. 75 00:06:17,380 --> 00:06:19,030 So let's call that angle up. 76 00:06:19,960 --> 00:06:23,350 That'll define this direction for us from the horizontal. 77 00:06:24,340 --> 00:06:30,400 But to get that, we need to find this angle here and we can call it fine, and that we can do with 78 00:06:30,400 --> 00:06:31,230 a signed route. 79 00:06:31,930 --> 00:06:41,590 And we know that the Sindel says that the son of this divided by this equals the sign of this angle 80 00:06:41,590 --> 00:06:43,330 divided by that length of there. 81 00:06:44,770 --> 00:06:52,630 So what I can say is that the sign of this angle, which you're interested in science over this length, 82 00:06:53,260 --> 00:07:01,410 then as equal to the sign of this angle of a year, which is 75 signs. 83 00:07:01,480 --> 00:07:06,310 Seventy five over this length of there, which is the one with the we just calculated fifteen point 84 00:07:06,310 --> 00:07:06,790 seven. 85 00:07:07,870 --> 00:07:16,420 OK, and now I could just solve for sign find and I can take the inverse of that and I can get that 86 00:07:16,420 --> 00:07:25,480 five our angle there, that angle of the there is thirty seven point eight, nine degrees. 87 00:07:26,050 --> 00:07:34,800 OK, now I want that angle between that vector, the A, B and the horizontal. 88 00:07:34,810 --> 00:07:43,760 So we just need to subtract our angles from each other and then we can find that relative angle. 89 00:07:44,140 --> 00:07:53,440 So what we know is that this is 45 and this is the horizontal it's side and that is also horizontal. 90 00:07:53,650 --> 00:07:58,500 So if you go like this, this whole angle of the year must be 45 as well. 91 00:07:58,520 --> 00:07:58,810 Right. 92 00:07:59,290 --> 00:08:04,650 So we know that that angle there is just going to be 45 degrees, minus five. 93 00:08:05,020 --> 00:08:16,570 So Seeta is 45 degrees, minus thirty seven, eight, nine degrees, and therefore firing is seven one 94 00:08:16,570 --> 00:08:18,160 one degrees. 95 00:08:18,710 --> 00:08:25,180 OK, and that defines our the a relative to the.