A ball moving with a velocity `v` hits a massive wall moving towards the ball with a velocity a. An elastic impact lasts for time `/_\t`

Options

A. The average elastic force acting on the ball is `(m(u + v))/(Deltat)`
B. The average elastic force acting on the ball is `(2m(u + v))/(Deltat)`
C. The kinetic energy of the ball increases by `2m u(u + v)`
D. The kinetic energy of the ball remains the same after the collision

Answer

B, C

Explanation

`p_(1) = -mv , p_(f) = m(v + 2u) :. Deltap = 2m(v + u)`
`:.` Force `= (Deltap)/(Deltat) = (2m(v + u))/(Deltat)`
`KE_(1) = (1)/(2)mv^(2) , KE_(F) = (1)/(2)m (2u + v)^(2)`
`DeltaKE = K_(f) - K_(1)`
`= (1)/(2) m (4u^(2) + v^(2) + 4uv - v^(2))`
`= (1)/(2)m [4u(v + u)]`
`= 2m u (v + u)`