A boy throws a rubber ball vertically downwards. He wants the ball to rebound from the floor and touch the ceiling of the room which is at a height of 5m. The coefficient of restitution is 0.9. With what velocity should the ball strike the floor?

Options

A. 8 m/s
B. 10 m/s
C. 11 m/s
D. 15 m/s

Answer

C

Explanation

For this collision,
`m_(1) u_(1) + m_(2)u_(2) = m_(1) v_(1) + m_(2)v_(2)`
`:. 1 xx 10 + 2 xx 5 = 1 xx (10 - 4) + 2 xx v_(2)`
`:. 10 + 10 = 6 + 2 v_(2)`
`:. 2 v_(2) = 20 - 6 = 14`
`:. v_(2) = 7 m//s` and `v_(1)= 6 m//s `
`:.` The coefficient of restitution
`e = ( v_(2) - v_(1))/( u_(1) -u_(2)) = ( 7-6)/( 10-5)= (1)/( 5) = 0.2 `