Question

A ball is dropped vertically from a height of 3.6m.It rebounds from a horizontal surface to a height of 1.6m.Find the coefficient of restitution of the material of the ball.​

Answer 1

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Answer 2

Motion

Height from which ball is dropped$=3.6 \ m$

Height to which ball rebounds $= 1.6\ m$

Taking the value of g as 10.

Velocity of ball when it reached the ground $= \sqrt{2gh}=\sqrt{2\times10\times3.6}=\sqrt{72}\ m/s$

After bounce off , the velocity will become $= e\sqrt{2gh}$$=e\sqrt{72}\ m/s$

$H_{max}=\frac{u^2}{2g} =1.6$

$\implies H_{max}=\frac{e^2\times72}{2\times10} =1.6$

$\implies e=\sqrt{\frac{32}{72} }=\sqrt\frac{4}{9} =\frac{2}{3}$

So, coefficient of restitution is $\frac{2}{3}$.