Question

A ball is dropped from a height $h$. It rebounds from the ground a number of times. Given that the coefficient of restitution is $e$. To what height does it go after $n^{th}$ rebounding?

• A. $\frac{h}{e^n}$
• B. $\frac{h}{e^{2n}}$
• C. $h{e}^n$
• D. $h{e}^{2n}$

Answer 1

Answer: (D)

$h{e}^{2n}$

Let, $h_n$ be the height it goes after $n^{th}$ rebounding
For $n^{th}$ rebounding, the coefficient of restitution is
$e^n=\sqrt{\frac{h_n}{h}}$
$e^{2n}=\frac{h_n}{h}$
$h_n=h{e}^{2n}$