Question

A ball is dropped from a height of $45\text{m}$ from the ground. The coefficient of restitution beween the ball and the ground is $\frac{2}{3}$. What is the distance in m travelled by the ball in 4th second of its motion? Assume negligible time is spent in rebounding. Let $g=10m/s^2.$

Answer 1

Time taken to fall through $45m=\sqrt{\frac{2\times 45}{10}}=3s$

$u_1=\sqrt{2gh}=\sqrt{2\times 10\times 45}=30\text{m/s}$
$u_2=e{u}_1=\frac{2}{3}\times 30=20\text{m/s}$
Distnace travelled in the fourth second = distance travelled in 1 s after rebounding $=20\times 1-\frac{1}{2}\times 10(1{)}^2=15m$