Question

A plastic ball falls from a height of $4.9$ metre and rebounds several times from the floor. What is the coefficient of restitution during the impact with the floor if $1.3$ seconds pass from the first impact to the second one?

• A. $0.9$
• B. $0.1$
• C. $0.7$
• D. $0.8$

Answer 1

The correct option is B $0.1$

As, $t=\sqrt{\frac{2h}{g}}$

Velocity of ball just before collision $=v=\sqrt{2gh}$

After first collision,

Velocity $=v_1=ev=e\sqrt{2gh}$

So, $t_1=\frac{v_1}{g}=e\sqrt{\frac{2h}{g}}$

So, time for second collision will be

$T=t+2t_1$

$=(1+2e)\sqrt{\frac{2h}{g}}$

Putting, $T=1.3sec.,h=4.9m$

$1.3=(1+2e)\sqrt{\frac{2\times 4.9}{9.8}}$

$1.3=1+2e$

$0.3=2e$

$e=0.1$