Question

A ball is dropped at a height of h measured from the ground. If the coefficient of restitution between the ball and the ground is e (between zero and one), what is the maximum height to which the ball rises after the first bounce?

Answer 1

The maximum height is
`he^2`.

Explanation:

The ball has been dropped from the height of h.

Let, the ball will be able to rise a height of H after first bounce.

The initial velocity of the ball is
`√(2gh)` and the velocity after the first bounce is
`√(2gH)`.

The coefficient of restitution, e =
`(√(2gH) )/(√(2gh) )` {as per the definition of coefficient of restitution}.

Hence, H =
`he^(2)`.