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Q.
A ball of mass $M$ falls from a height h on a floor and its coefficient of restitution is $e$. The height attained by the ball after two rebounds is
Work, Energy and Power
Solution:
A ball falling from height h reaches the floor with velocity
$v = \sqrt{2gh}$
By definition
$e = \frac{\text{velocity of separation}}{\text{velocity of approach}}$
$\therefore $ Rebound velocity $= e\sqrt{2gh}$
$\therefore $ Rebound height $= e^{2}h$
After two rebounds, height $= e^{4}h$