Physics cannon question

Question

A cannon of mass 6.66 x 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a 74.0-kg shell horizontally with an initial velocity of 590 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of a shell fired from this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system.)

Answer 1

Use conservation of momentum, and the given condition on energy to build two equations.

using m and v for the ball, and M and V for the cannon.

mv+MV=0

1/2mv^2+1/2MV^2=1/2m*590^2