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
$h=ut+\frac{1}{2}g{t}^2$
when $u=0,t=\sqrt{\frac{2h}{g}}$
The second impact occurs after an additional
time $=2\sqrt{2h_{1}g}=2e\sqrt{2h/g}$
$\left(\because h_1=e^{2}h\right)$
The third impact occurs after an additional
time $=2\sqrt{2h_{2}g}=2e^2\sqrt{2h/g}=e^2\sqrt{8h/g}$
$\left(\because h_2=e^{4}h\right)$