Question

A cannonball is fired from a cannon so that the cannon recoils backwards as the ball is fired forward. Identify which of the following statements is true about the cannonball & cannon?

• A. The velocity of the cannonball is equal and opposite to the velocity of the cannon
• B. The mass of the cannonball and the cannon must be equal
• C. The momentum of the cannonball must be greater than the magnitude of the momentum of the cannon
• D. The momentum of the cannon must be equal to the magnitude of the momentum of the cannonball.
• E. The momentum of the cannon must be greater then the magnitude of the momentum of the cannonball.

Answer 1

The correct option is D The momentum of the cannon must be equal to the magnitude of the momentum of the cannonball.

Since no external force acts on the cannon-cannonball system, there is no change in the total momentum of the system.

Hence the momentum of system before firing is equal to that after firing.

Initially momentum of system is zero.

Thus $0=\overrightarrow{P_{cannon}}+\overrightarrow{P_{cannonball}}$

$⟹\left|\overrightarrow{P_{cannon}}\right|=\left|\overrightarrow{P_{cannonball}}\right|$