Answer :
Final answer:
The recoil velocity of the cannon is approximately -4.37 m/s, calculated using the conservation of momentum, where the momentum before firing (cannon and cannonball at rest) is equal to the momentum after firing (cannonball moving forward and cannon recoiling backwards).
Explanation:
The recoil speed of a cannon or any other firearm is a consequence of the conservation of momentum. In the given scenario, we must use the principles of conservation of momentum to find the recoil speed of a cannon after it fires a cannonball. The momentum of the system (cannon and cannonball) must remain constant, assuming no external forces influence it (ignoring air resistance and friction). Therefore, the momentum before firing is equal to the momentum after firing.
Before the cannon fires, the system is at rest, so the total momentum is 0. After the cannon fires, the momentum of the cannonball is its mass multiplied by its velocity, while the momentum of the cannon is its mass multiplied by its recoil velocity. We use the formula:
Mass of cannon × Recoil velocity of cannon = - (Mass of cannonball × Velocity of cannonball)
Recoil velocity of cannon = - (Mass of cannonball × Velocity of cannonball) / Mass of cannon
Plugging in the given values:
Recoil velocity of cannon = - (12 kg × 126 m/s) / 346 kg
Recoil velocity of cannon = - (1512 kg·m/s) / 346 kg
Recoil velocity of cannon = - 4.37 m/s (approximately)
The negative sign indicates the direction of the recoil is opposite to the direction of the cannonball's velocity.
