When fired from a gun, a projectile weighing 20 kg takes off at a speed of 800 m / s.

When fired from a gun, a projectile weighing 20 kg takes off at a speed of 800 m / s. What is the recoil speed of the gun barrel if its mass is 2000 kg? The initial velocity of the gun is zero.

mс = 20 kg.
Vs “= 800 m / s.
mo = 2000 kg.
Vo “-?
Since the gun interacts only with the projectile, the gun-projectile system can be considered closed.
For a closed system, the momentum conservation law is valid: the sum of the impulses of a closed system does not change.
(mo + mc) * V = mo * Vo “+ mc * Vc”.
Since before the shot the gun with the projectile was at rest V = 0 m / s, the law of conservation of momentum will take the form: mo * Vo “+ mc * Vc” = 0.
mо * Vо “= – mс * Vс”.
Vо “= – mс * Vс” / mo.
The “-” sign indicates that after firing the gun will move in the opposite direction of the projectile’s departure.
Vo “= 20 kg * 800 m / s / 2000 kg = 8 m / s.
Answer: after firing, the gun will move in the opposite direction of the projectile departure with a speed of Vо “= 8 m / s.