Question

The adjacent figure shows an infinite frame of two sides in a gravity-free space. What is the final constant kinetic energy expected of the ball of mass $m$ projected as shown with an initial velocity $v_{0}$ ? The coefficient of restitution for the collision between the ball and the frame is $e=\text{0.5}$ .

• A. $\text{0.5}mv_{0}^{2}$
• B. $\text{0.25}mv_{0}^{2}$
• C. $\text{0.125}mv_{0}^{2}$
• D. $\text{0.325}mv_{0}^{2}$

Answer 1

Answer: (B)

The component $v=v_{0}sin45^\circ =\frac{v_{0}}{\sqrt{2}}$ perpendicular to the walls is finally lost after a long time.
Hence, final remaining $K.E.=\frac{1}{2}m\left(\frac{v_{0}}{\sqrt{2}}\right)^{2}$