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