Question

A ball is dropped from a height of $1m$. The coefficient of restitution between the ground and the ball is $1/3$. The height to which the ball will rebound after two collisions with ground is :

• A. $9m$
• B. $1/9m$
• C. $1/81m$
• D. $81m$

Answer 1

Answer: (C)

$1/81m$

Height upto which the ball rebound after nth collision , $H_n=e^{2n}{H}_{initial}$

Given : Coefficient of restitution $e=\frac{1}{3}$ $H_{initial}=1$ m

Let the height upto which the ball rebound after two collisions be $H_2$

$\therefore$ $H_2=e^{2\times 2}\times 1=e^4$

$⟹H_2=(\frac{1}{3}{)}^4=\frac{1}{81}$ $m$