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

Answer 1

Answer: (C)

$e^{4}h$

Answer 2

A ball falling from height h reaches the floor with velocity

$v = \sqrt{2gh}$

By definition

$e = \frac{velocityofseparation}{velocityofapproach}$

$\therefore$Rebound velocity =$e\sqrt{2gh}$

$\therefore$Rebound height = e²h

After two rebounds, height = $e^{4}h$