Final answer:
The recoil velocity of the cannon is -0.45 m/s.
Step-by-step explanation:
To determine the recoil velocity of the cannon, we can use the law of conservation of momentum. The initial momentum of the cannon and cannonball system is zero, since they are initially at rest. After firing, the momentum of the cannonball is given by the product of its mass and velocity, and the recoil velocity of the cannon is given by the negative of this momentum divided by the mass of the cannon.
So, the recoil velocity of the cannon can be calculated using the formula:
Vcannon = -(mcannonball * Vcannonball) / mcannon
Substituting the given values:
Vcannon = -(3 kg * 75 m/s) / 500 kg = -0.45 m/s
Therefore, the recoil velocity of the cannon is -0.45 m/s.