A gun of mass M fires a bullet of mass m 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.

Explanation

Let v: speed of (gun/mirror) just after firing By momentum conservation
`mV=Mvimpliesv=(m)/(M)V`
velocity of bullet w.r.t. mirror
`V+v=(1+(m)/(M))V`, towards left
Velocity of image of bullet
`V+v=(1+(m)/(M))V`, towards right
(when object is at pole, velocity of object and image are equal)
The velocity of image with respect to bullet
`v_r=(V+v)+(V+v)`
`=2(1+(m)/(M))V`