Answer to Question #236176 in Atomic and Nuclear Physics for Sohit

Question

A ball is moving with speed 12 m/s towards a heavy wall which is moving towards the ball with the speed 10 m/s as shown in figure. Assuming collision to be perfectly elastic, find the speed of ball after the collision.

12 m/s

10 m/s

Answer 1

Since the wall is heavy, its velocity will not change after the collision. Then, we can find the speed of the ball after the collision from the definition of the coefficient of restitution:

$$\dfrac{-(v_{ball,f}-v_{wall,f})}{v_{ball,i}-v_{wall,i}}=e,$$

here, $e=1$ is the coefficient of restitution for the perfectly elastic collision.

Then, we get:

$$\dfrac{-(-v_{ball,f}-(-10\ \dfrac{m}{s}))}{12\ \dfrac{m}{s}-(-10\ \dfrac{m}{s})}=1,$$ $$\dfrac{v_{ball,f}-10\ \dfrac{m}{s}}{22\ \dfrac{m}{s}}=1,$$ $$v_{ball,f}=32\ \dfrac{m}{s}.$$

Answer:

$v_{ball,f}=32\ \dfrac{m}{s},$ away from the wall.