A Cannon

A cannon of mass 1000 kg fires a 10-kg shell at a velocity of 200 m/s. At what speed does the cannon recoil?

The law of conservation of momentum tells us that

p_cannon,i + p_shell,i = p_cannon,f + p_shell,f .

Choosing a coordinate system in which the cannon points in the positive direction, the given information is

p_cannon,i = 0

p_shell,i = 0

p_shell,f = 2000 kg·m/s .

We must have p_cannon,f = -2000 kg·m/s, so the recoil velocity of the cannon is -2 m/s.