Q. A ball is dropped from a height of $45\, m$ 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 $g=10\, m s ^{2}$.
Work, Energy and Power
Solution:
Time taken to fall through $45\, m =\sqrt{\frac{2 \times 45}{10}}=3\, s$
$u_{1}=\sqrt{2 g h}=\sqrt{2 \times 10 \times 45}=30\, m / s$
$u_{2}=e u_{1}=\frac{2}{3} \times 30=20\, m / s$
Distance travelled in the fourth second = distance travelled in $1\, s$ after rebounding $=20 \times 1-\frac{1}{2} \times 10(1)^{2}=15 m$
