Question

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

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

Answer 1

The Correct Option is 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,$v=\sqrt{2gh_1}$ $e=\frac{v}{u}=\sqrt{\left(\frac{h_1}{h}\right)}$ 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, $h_1, = e^2h, h_2 = e^4h$ ... and so on. Similarly, after nth rebound $h=e^{2n}h$