Question

A ball is dropped from a height $100m$ on the ground. If the coefficient of restitution is $0.2$, the height to which the ball will go up after it rebounds for the IInd time

• A. $15m$
• B. $1.6cm$
• C. $1.6m$
• D. $40cm$

Answer 1

The correct option is D $40cm$

Velocity gained after falling a height equal to $h_1=100m$ is $V_1=\sqrt{2g{h}_1}=\sqrt{20\times 100}=10\sqrt{2}m/s$

so velocity with which it will rebound will be $V_2=e\times V_1$, where $e$ is the restitution coefficient.

so $V_2=0.2\times 10\sqrt{2}=2\sqrt{2}m/s$

the new height reached will be $h_2=\frac{V_2^2}{2g}=\frac{8}{20}=0.4m$