Question

A body falls on a surface of coefficient of restitution $.6$ from a height of $1m$. Then the body rebounds to a height of:

• A. $0.6m$
• B. $0.4m$
• C. $1m$
• D. $0.36m$

Answer 1

Answer: (D)

$0.36m$

from Energy conservation

$mgh=\frac{1}{2}m{v}^2$

where v is velocity by which ball rebound

to calculate $v$, we need to know $u$ by which ball hit ground.

$mg\left(1\right)=\frac{1}{2}m{u}^2$

$u^2=2g$

and $e=\frac{v}{u}$

$v^2=e^2{u}^2=e^2\times 2g$

for final height:

$mgh=\frac{1}{2}m{v}^2$

$h_n=h{e}^2=1\times e^2=1\times (0.6{)}^2=0.36m$