Question

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

• A. 5 m
• B. 20 m
• C. 15 m
• D. 10 m

Answer 1

Answer: (C)

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