Question

A body from height $h$ is dropped. If the coefficient of restitution is $e$, then calculate the height achieved after one bounce

• A. $h_1=e^{2}h$
• B. $h_1=e^{4}h$
• C. $h_1=eh$
• D. $h_1=\frac{h}{e}$

Answer 1

Answer: (A)

When a body falls from a height h, it strikes the ground with a velocity $u=\sqrt{2gh}$. Let it rebounds with a velocity v and rise to a height $h_1$
Therefore,$v=\sqrt{2g{h}_1}$
$e=\frac{v}{u}=\sqrt{\left(\frac{h_1}{h}\right)}$
If the successive heights to which the body rebounds again and again and $h_2,h_3$,..., then
$e=\sqrt{\frac{h_1}{h}}=\sqrt{\frac{h_2}{h_1}}=\sqrt{\frac{h_1}{h_2}}=...$
Clearly, $h_1,=e^{2}h,h_2=e^{4}h$ ... and so on.
Similarly, after nth rebound
$h=e^{2n}h$