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.
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Sol. From conservation of linear momentum, we get
MV' = mV
∴ V' = 
Just after the bullet is fired,
u → 0
∴ m = magnification = 
= 1
We know that 
= – m 2 
= 
– 
= V – (– V') = V 
Now, 
= – 
Hence, speed of separation between bullet and its image will be 2V 
.
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