Question

A ball after falling freely from a height of $4.9\, m$ strikes a horizontal plane. If the coefficient of restitution is $ \frac{3}{4}, $ the ball will strike second time $4$ with the plane after

• A. $ \frac{1}{2}s $
• B. $ 1\,s $
• C. $ \frac{3}{2}s $
• D. $ \frac{3}{4}s $

Answer 1

Answer: (C)

Time taken by the ball to reach the plane
$t=\sqrt{\frac{2 h}{g}} $
$=\sqrt{\frac{2 \times 4.9}{9.8}}=1\, s$
Height attained by the ball after $1^{st}$ bounce
$h=e^{2} h $
$=\left(\frac{3}{4}\right)^{2} \times 4.9$
$\frac{1}{2} g t^{2}=\frac{9}{16} \times 4.9$
$t=\sqrt{\frac{2 \times 9 \times 4.9}{16 \times g}}$
$=\sqrt{\frac{18 \times 4.9}{16 \times 9.8}}=\frac{3}{4} s$
So, the ball will strike second time after
$=2 \times \frac{3}{4}=\frac{3}{2} s$