A small block of mass m and a concave mirror of radius R fitted with a stand lie on a smooth horizontal table with a separation d between them. The mirror together with its stand has a mass m. The block is pushed at t = 0 towards the mirror so that it starts moving towards the mirror at a constant speed V and collides with it. The collision is perfectly elastic. Find the velocity of the image (a) at a time `t lt d/V,` (b) at a time `t gt d/V`.

Options

A. `(-R^2 V)/([2(d-Vt)-R]^2) . V (1+(R^2)/([2(Vt - d) -R]^2) )`
B. `(R^2 V)/([2(d+Vt)+R]^2) . V (1+(R^2)/([2(Vt - d) -R]^2) )`
C. `(-R^2 V)/([2(d-Vt)-R]^2) . V (1-(R^2)/([2(Vt - d) +R]^2) )`
D. `(-R^2 V)/([2(d-Vt)-R]^2) . V (1-(R^2)/([2(Vt + d) -R]^2) )`

Answer

A