Question

A ball is dropped from a height $h$ above a tile floor and rebounds to a height of $0.64h$. The coefficient of restitution between the ball and the floor is

• A. $0.64$
• B. $0.8$
• C. $1/0.64$
• D. $1/0.8$

Answer 1

Answer: (B)

$0.8$

Let the velocity with which ball strikes the floor & rebounds be v and v' respectively.
Using energy conservation:

$mgh=\frac{1}{2}m{v}^2-\left(1\right)mg\left(0.64h\right)=\frac{1}{2}m{v^{\prime }}^2-\left(2\right)$

Using (1) & (2)

$\frac{0.64}{1}=\frac{{v^{\prime }}^2}{v^2}$
$\Rightarrow \frac{v^{\prime }}{v}=0.8$

Therefore coefficient of restitution is $0.8$