A shell of mass 0.020 kg is fired by a gun of mass 100 kg.  If the muzzle speed of the shell is $80 m{s}^{-1}$  , what is the recoil speed of the gun?

Here, mass of the shell,  $m_1= 0.02 kg$ ; mass of the gun,  $m_2= 100 kg$ ; Initial velocities of both the shell and the gun are zero i.e.  $u_1=u_2=0$ After firing, speed of the shell, $v_1=80m{s}^{-1}$ Let $v_2$ be  the recoil speed of the gun.  According to the principle of conservation of momentum.

$m_1{v}_1+m_2{v}_2=m_1{u}_2+m_2{u}_2$

$\therefore 0.02\times 80+100v_2=0.02\times 0+100\times 0$

or   $v_2=-\frac{0.02\times 80}{100}=-0.016m{s}^{-1}$