. A rubber ball dropped from a height of 20m (g=10m/s2) falls on the roof of an elevator
going up at 2 m/s. If the collision of the ball
with the elevator is elastic, the ball
rebounds with a velocity of

24 m/s

Explanation:

Given that the height of the ball from the elevator, h=20 m

The acceleration due to gravity, g=10 m/

The initial velocity of the ball is zero, so, by using the equation of the motion the velocity of the ball, v, when reached the elevator,

m/s

The velocity of the ball just before the collision is 20 m/s in the downward direction.

The velocity of the lift just before the collision is 2 m/s in the upward direction.

As the ball and the lift moves in the opposite direction, so the speed of approach m/s.

Assuming that there is negligible change in the speed of the lift, so the velocity of the lift after the collision is 2 m/s

Let the velocity of the ball after the collision is m/s in the direction of the velocity of the lift.

So, the speed of the separation

As the collision is elastic, so the coefficient of restitution,

m/s

Hence, the ball rebounds with a velocity of 24 m/s.

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