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a small ball falling vertically down with velocity 2m/s strikee elastically an inclined plane moving with velocity 2m/s.calculate velocity of rebound ball with respect to ground.

a small ball falling vertically down with velocity 2m/s strikee elastically an inclined plane moving with velocity 2m/s.calculate velocity of rebound ball with respect to ground.

Grade:10

2 Answers

Ashish Kumar
askIITians Faculty 32 Points
7 years ago

As the masses of the ball and plane are not given,and as it given in the question that the ball is small , we assume it as the collision between the heavy body (inclined plane ) and light body (ball).

In the horizontal direction the heavy body is moving but the ball has no horizontal momentum.There fore after collision the horizontal velocity of plane will almost be the same but the ball will have horizontal velocity double that of the plane ,ie, Vx=4 m/s.

In the vertical direction as the plane has no component in this direction it is at rest in the vertical direction.So the ball will rebound back with the same vertical velocity it had before the collision ,ie, Vy=2 m/s.

So total velocity of ball     V=sq root(4^2+2^2)= 4.47 m/s

 

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Ashish Kumar
askIITians Faculty 32 Points
7 years ago
As the ball is small , we will consider the situation as a collision of the heavy body (inclined plane) and a light body (ball). In the vertical direction there is no velocity of the plane so the ball rebounds back with the same vertical speed= 2 m/s. In the horizontal direction the inclined plane has velocity but the ball has no horizontal component of velocity. So the ball will rebound with twice the horizontal velocity of the inclined plane = 2 *2 =4 m/s.
Therefore total velocity = sq. root( 4 ^2 + 2 ^2 ) = sq. root 20.



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