00:02
In this problem, an aeroplane is flying horizontally with a speed of 500 km per hour and it is flying at a height of 800 meter.
00:12
Now it drops a crate at certain location and the parachute of the crate fails to open.
00:21
Because of that it follows a trajectory motion and it hits the ground at certain distance.
00:28
So we have to calculate after how much distance it is a way much distance it is a very much distance.
00:32
Going to hit the ground so basically we have to calculate value of x here all right so what are the given quantities so any velocity of the aeroplane was 500 km per hour so first we will convert this into s i unit so 500 kilometer per hour we need to multiply it by 1 000 divided by a 3 ,600.
01:03
So, after multiplying this factor, this velocity will convert into meter per second.
01:08
So the velocity comes out to be 1 ,250 divided by 9 meter per second.
01:17
All right.
01:18
So this was the velocity of the aeroplane.
01:21
Now, whenever an object is dropped from a moving object, in that case, velocity of the moving object is transferred to the velocity of the dropped object.
01:32
And this happens because of the newton's first law of motion.
01:35
Actually, this happens because of inertia.
01:38
And inertia is defined in the newton's first law of motion.
01:41
So, the block will receive a horizontal speed.
01:45
Let us say this is the x, this is x direction and this is y direction.
01:49
So, block will have a horizontal speed that is vx, that is equals to v, which is 1 ,250 upon 9 meter per second.
02:00
So with this speed, the block is falling on the ground.
02:05
Now, what is the acceleration of the block? since there is no parachute, it means that there is no drag force.
02:11
So only acceleration that this block will have, that will be the acceleration due to gravity under the free fall.
02:18
So this block will have an acceleration only in y direction, since gravity will act in vertical direction so a y is 9 .8 meter per second square all right what will be the initial velocity of block uh in the y direction so initial velocity of block in wide direction will be zero since the aeroplane was moving horizontally therefore the block will have initial velocity completely in the horizontal direction there will be no velocity component in y direction so velocity of the block in y direction is zero meter per second and velocity of block box in x direction is 1250 upon 9 meter per second now what are the what are the other canymetic parameters in y direction so acceleration in y direction is 9 .8 meter per second square and displacement in y direction is 800 meter so can we find what will be the time required for this block to cover the vertical height of 800 meter so, we have to use a kinematic relation that will relate these four parameters, that is velocity, acceleration, displacement and time.
03:36
And the relation is, s y is equals to v0y into t plus half a y into t square...