Question

A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is:

• A. $e^{2}h$
• B. $e{h}^2$
• C. $e^{4}h$
• D. $\frac{h}{e^4}$

Answer 1

The correct option is C $e^{4}h$

A ball falling from height $h$ reaches the floors 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, $height=e^{4}h$.