A gun of mass *M* fires a bullet of mass with a horizontal speed *V*. The gun is fitted with a concave mirror of focal length *f* facing towards the receding bullet. Find the speed of separation of the bullet and the image just after the gun was fired.

the focal length of the concave mirror = f

Mass of the gun= M

Horizontal speed of the bullet= V

Let the recoil speed of the gun= V_{g}

Using conservation of linear momentum,

At time t= t

The object distance from the mirror, u= -(Vt-t)

Focal length, f= -f

Image distance from the lens, v=?

By using mirror formula,

The separation between the image of bullet and the bullet at time t I given by

Differentiating the equation with respect to t, we get

Therefore, the speed of separation of the bullet and image just after the gun was fired is

1