Question

A ball is dropped from a height of 1 m. if coefficient of restitution between the surface and the ball is 0.6, the ball rebounds to a height of

• A. 0.6 m
• B. 0.4 m
• C. 1 m
• D. 0.31 m

Answer 1

The correct option is D 0.31 m

Coeeficient of Restitution (COR) is the ratio of the final to initial relative velocity between two objects after they colloid.

$COR\left(e\right)=\frac{Relativevelocityafter}{}collisionRelativevelocitybeforecollision\to \left(i\right)$

A/Q $Height\left(s\right)=1m,e=0.6$

Velocity just before ball touches the ground can be found with newtons law of motions

$v^2=u^2+2as$

We have $u=0$ So, $V=\sqrt{2gs}\Rightarrow v=\sqrt{2g}\to \left(ii\right)$
Now, from $\left(i\right)$

$e=\frac{V_{after}}{V_{before}}{V}_{after}=2\times V_{before}\to \left(iii\right)$
Now, rebounded height can again be calculate with equation of motions

$v^2=u^2+2as$

Now, $u=v_{after}=ev;v=0;a=-g;s=?\Rightarrow s=-\frac{u^2}{2a}\Rightarrow s=\frac{(ev{)}^2}{2g}\Rightarrow s=\frac{e^{2}2g}{2g}\Rightarrow s=e^2\Rightarrow s=0.36$