Question

An elastic ball is dropped from a height $h$ and it rebounds many times from the floor. If the coefficient of restitution is $e$, the time interval between the second and the third impact, is:

• A. $ \frac{ev}{g} $
• B. $ \frac{e^{2}v}{g} $
• C. $ e^{2}\sqrt{\left( \frac{8h}{g} \right)} $
• D. $ e^{2}\sqrt{\left( \frac{h}{g} \right)} $

Answer 1

Answer: (C)

Assume, initial velocity to be zero. From equation of motion
$h=u t+\frac{1}{2} g t^{2}$
when $u=0, t=\sqrt{\frac{2 h}{g}}$
The second impact occurs after an additional
time $=2 \sqrt{2 h_{1} g}=2 e \sqrt{2 h / g}$
$\left(\because h_{1}=e^{2} h\right)$
The third impact occurs after an additional
time $=2 \sqrt{2 h_{2} g}=2 e^{2} \sqrt{2 h / g}=e^{2} \sqrt{8 h / g} $
$\left(\because h_{2}=e^{4} h\right)$