First slide

Coefficient of restitution

Question

A ball is dropped from a height h above a floor. If the coefficient of restitution between the floor and the ball is e, the ball after the first rebound will rise to a height of

Moderate

A

eh
B

e² h
C

h/e
D

h/e²

Solution

Let u and u' be the speeds of the ball before and after striking the floor respectively. Then
$e = u^{'} / u or u^{'} = eu$
Now $u = \sqrt{(2 gh)} and u^{'} = \sqrt{(2 {gh}^{'})}$
Where h' is the height to which the ball rises after rebound.
$∴ \frac{u}{u^{'}} = \frac{\sqrt{h}}{\sqrt{h^{'}}} or h^{'} = \frac{u^{' 2}}{u^{2}} \times h = e^{2} h$

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