00:01
Hello students, in this question we have a helicopter.
00:04
So, helicopter starts from point a to point b.
00:09
From mass surface it transfers.
00:12
So, it travels a distance of d starting from time t is equal to minus t.
00:22
So, we are given a function of acceleration a of t is equal to minus beta t by t x cap plus alpha 2t square 2t cube by 3t square minus t raise to 5 by t raise to 5 in the y cap direction.
00:54
So, this is the acceleration and we are given the velocity v of t is equal to minus beta t square divided by 2t plus v i x in the x cap direction plus alpha times t raise to 4 by 6 t square 6 t cube minus t raise to 6 by 6 t raise to 5 plus v i y in the y cap direction.
01:34
So, we got the velocity and acceleration.
01:36
Now, to find out the distance, the distance we can write down.
01:42
The distance will be the integral of velocity, right? that will be the distance displacement x of t.
01:51
So, integral with respect to t will be equal to, you can do it separately individually.
01:58
So, you can write down beta integral of t square is equal to 2t square 2t by 2t plus, so 2 and 2 cancels.
02:09
Integral of that will be equal to sorry t cube by 3.
02:16
This is the differential.
02:23
Okay, so that will be equal to t cube by 3 times 2 that is 6t plus v i n times t right? in the x cap direction plus alpha t raise to 5 by 30 t cube minus t raise to 7 by 42 t raise to 5 plus v i y times t in the y cap direction.
03:02
Right? that is the displacement for the object.
03:05
Now, we know that the distance travelled by that thing is d, right? by the helicopter is d.
03:13
So, you simply can put down that the distance is equal to d.
03:17
So, this is equal to d.
03:20
That means you can simplify now.
03:22
D in the x cap direction dx plus dy in the y cap direction is equal to this thing.
03:32
So, dx will be equal to minus d t cube by, so this happens in the x cap direction, right? horizontal, there is no horizontal velocity displacement after because it is travelling in a straight line in a horizontal distance.
03:53
So, what it means is that the vertical component will become 0.
03:57
Dy is equal to 0.
03:59
So, this will be dx or d.
04:02
Right? that will be d.
04:02
Dx will be equal to d.
04:05
T cube by 6t plus v i n times t.
04:11
So, that will be equal to that...