00:01
Hello, in the question we have given that a coast guard cutter detects an unidentified ship at a distance of 16 kilometers.
00:11
So, let's say here we have this coast guard.
00:15
So, he identifies a ship over here.
00:19
So, this angle is 15 degrees.
00:23
Sorry.
00:25
So, this angle out here is 15 degrees.
00:31
And so, see over here, we have the ship.
00:35
So, this is 16 kilometers.
00:39
So, this vector we have it is of 16 kilometers.
00:42
Then further, the ship is traveling at 30 kilometer per hour on course at 40 degrees east of north.
00:54
So, it is traveling with a speed.
00:56
So, this angle if i want to show this angle.
01:00
So, it will be so this angle out over here is 40 degrees and this ship is moving with a speed of 30 kilometer per hour.
01:17
So, the coast guard wishes to send a speed boat to intercept and investigate the vessel.
01:28
So, we have to find the following things.
01:32
So, from here he sends a speed boat.
01:37
So, it should intercept over here.
01:41
So, now in order to do this, in order to solve this problem.
01:45
So, this is a vector we have.
01:47
So, we have 16 kilometers.
01:49
So, let us call this angle as angle phi and let us call this bearing angle as theta.
01:58
So, this angle is theta and this speed is of 58 kilometer per hour.
02:07
So, now if i draw if i extend this, so this is so this angle will be 15 and so it will be 40.
02:18
So, 180 degree will be equal to 40 plus theta.
02:32
But now this theta extends until here.
02:36
So, i will minus this 15.
02:38
So, this will be minus 15.
02:40
So, theta i will get 180 minus 40 plus 15.
02:47
So, theta will be equal to 155 degrees.
02:51
So, this angle we got it as 155 degrees.
02:56
Now, in order to find out the angle, so they are asking that if a speed boat travels at 58 kilometer per hour, in what direction should it head? so, we have to find out the direction of the speed boat, that is this entire angle.
03:14
So, this will be angle phi plus 15 degree.
03:18
Now, in order to do this, we need this is the distance...