Question

A ball is dropped from height h on the ground level. If the coefficient of restitution is e then the height upto which the ball will go after $n^{th}$ jump will be-

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

Answer 1

Answer: (D)

$h{e}^{2n}$

Coefficient of restitution is
$e=\frac{v_2-v_1}{u_1-u_2}=\frac{\sqrt{2g{h}_1}}{\sqrt{2gh}}$
$\therefore e=\sqrt{\frac{h_1}{h}}$
Hence after first bouncing $h_1=h{e}^2$
after second $h_2=h{e}^4$
and so on after the nth bounce $h_n=h{e}^{2n}$