A 1385 kg cannon containing a 58.5 kg cannon ball is on wheels. the cannon fires the cannon ball giving it a velocity of 49.8 m/s north. what is the initial velocity of the cannon the instant after it fires the cannon ball?

Conservation of momentum requires that the sum of momenta after is equal to that before. Since initially nothing is moving, the sum after the shot will also add to zero.

m₁v₁ = - m₂v₂

Solve for the cannon's velocity v₁

v₁ = - m₂v₂/m₁ = - 2.10m/s

The negative sign means it's moving 2.10m/s south.