Is momentum conserved when a cannon is rigidly mounted to the deck of a large boat and subsequently fired. What will happen and why?

To determine whether momentum is conserved when a cannon is fired from a rigidly mounted position on the deck of a large boat, we need to evaluate the system before and after the firing.

Before the cannon is fired, the boat and the cannon are at rest. The net momentum of the system is zero because there is no motion. The cannonball inside the cannon also has zero momentum because it is not moving.

Now, when the cannon is fired, several things happen simultaneously. First, the cannonball is expelled from the cannon with a certain velocity in one direction. This creates a forward momentum in the cannonball. Second, the cannon experiences an equal but opposite backward momentum due to the reaction force from the cannonball being expelled. Third, as per Newton's third law, the boat experiences an equal and opposite momentum in the backward direction to maintain overall momentum conservation.

Therefore, momentum is indeed conserved in this situation. The forward momentum of the cannonball is balanced by the backward momentum of the cannon and the boat. As a result, the boat will recoil backward.

However, it's essential to note that while momentum is conserved, the overall velocity of the boat and cannon system may not be zero after the firing. The boat's recoil is determined by the mass of the cannonball, the velocity at which it is expelled, and the mass of the boat itself.