A bullet of mass 20 g is fired from a rifle of 8 kg with an initial velocity of 100 m/s. Find the final velocity of the recoil of the rifle.

Given, the initial momentum of system ${\mathrm{p}}_{\mathrm{i}}=0$

Momentum = Mass x Velocity

${\mathrm{m}}_1={\mathrm{m}}_{\mathrm{gun}}=8\mathrm{kg}$ ,

${\mathrm{m}}_2={\mathrm{m}}_{\mathrm{bullet}}=0.02 \mathrm{kg}$

${\mathrm{v}}_2={\mathrm{v}}_{\mathrm{bullet}}=100 \mathrm{m}/\mathrm{s}$

by applying, the conservation of momentum, the momentum of a system is constant if there is no external force on the system.

$\Rightarrow {\mathrm{m}}_1{\mathrm{v}}_1+{\mathrm{m}}_2{\mathrm{v}}_2=0$

$\Rightarrow 8\mathrm{v}+0.02\times 100=0$

$\Rightarrow \mathrm{v}=-0.25 \mathrm{m}/\mathrm{s}$

Therefore, the recoil velocity of the gun will be -0.25m/s. The negative direction signifies that the direction of the gun will be opposite to the direction of the bullet.