An object and a plane mirror are shown in figure. Mirror is moved with velocity `V` as shown. The velocity of image is :
.

Options

A. `2 V sin theta`
B. `2V`
C. `2V cos theta`
D. none of these

Answer

A

Explanation

`vec(V)_(I,M) = -vec(V)_(O,M)` (normal to plane mirror)
`rArr vec(V)_(1) - vec(V)_(M) = -(vec(V)_(0) - vec(V)_(M))`
`rArr V_(1) - V sin theta = - (0 - V sin theta)`
`rArr V_(1) = 2V sin theta`