A shell of mass 0.01 kg fired by a gun of mass 10 kg. If the muzzle speed of the shell is 50 ms^–1, what is the recoil speed of the gun?

Let the velocity of the gun be 'v_g'

As there are no external forces acting on the system of gun and bullet, the total linear momentum is conserved.

$\Rightarrow {\mathrm{m}}_{\mathrm{m}}{\mathrm{v}}_{\mathrm{m}}+{\mathrm{m}}_{\mathrm{g}}{\mathrm{v}}_{\mathrm{g}}=0$

$0.01 \mathrm{x} 50+10 \mathrm{x} {\mathrm{v}}_{\mathrm{g}}=0\Rightarrow {\mathrm{v}}_{\mathrm{g}}=0.05\mathrm{m}/\mathrm{s}$