A smooth sphere is moving on a horizontal surface with velocity vector `3hat(i) + hat(j)` immediately before it hits a vertical wall. The wall is parallel to the vector `hat(j)` and the coefficient of restitution between the wall and sphere is `(1)/(3)`. The velocity vector of the sphere after it hits the wall is :-

Options

A. `hat(i) + hat(j)`
B. `3hat(i) - (1)/(3) hat(j)`
C. `-hat(i) + hat(j)`
D. `hat(i) - hat(j)`

Answer

C

Explanation

`e ("Rate of seperation")/("Rate of approach")`
`(1)/(3) = (v_(x))/(3)`
`v_(x) = 1`
`v_(f) = -hat(i) + hat(j)`