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= Vg



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