Question

A shell of mass 10 kg is fired from a gun of mass 500 kg. The gun recoils with a velocity of 5 m/s. Find the muzzle velocity of the shell.

Answer 1

$m=10kg$, $M=500kg$, $v=5m/s$
Let V be the recoil speed of the gun.
According to the law of conservation of momentum,
Initial momentum = Final momentum
0 = mv + MV
$V=\frac{-mv}{M}=\frac{-\text{/}10\times \text{/}5}{500}=-0.1m/s$
Negative sign indicates that the gun moves backward as the bullet moves forward.