Question

A ball after falling freely from a height of $4.9m$ 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. $1s$
• C. $\frac{3}{2}s$
• D. $\frac{3}{4}s$

Answer 1

Answer: (C)

Time taken by the ball to reach the plane
$t=\sqrt{\frac{2h}{g}}$
$=\sqrt{\frac{2\times 4.9}{9.8}}=1s$
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
$=2\times \frac{3}{4}=\frac{3}{2}s$