m = 0.020 kg is the mass of the shell.
M is the gun’s mass, which is 100 kilogrames.
The shell’s speed is 80 m/s.
The shell’s and gun’s initial velocity is both zero. As a result, the system’s initial momentum is zero.
The beginning momentum is equivalent to the end momentum when the rule of conservation of momentum is applied.
So,
0 = MV
v = mv/M is the gun’s recoil speed.
(0.020 x 80)/100 = v
v = 0.016 m/s