At the circus, a 100-kilogram clown is fired 15 m/s from a 500-kg cannon.

Question

What is the recoil speed of the cannon?

Answer 1

This problem is under the application of the conservation of momentum. It states that all the momentum in the system at one state will be equal to all the momentum in the system at any other state so long as no outside forces or influences interact with the system.

In equation form:

∑p_i = ∑p_f

Commonly, these problems involve an initial state and a final state. No other states will be considered. Final is measured just as the clown is jettisoned from and leaves the head of the cannon.

In the initial state, nothing is moving. The cannon is stationary and the clown is resting in the cannon.

Thus, ∑p_i = 0.

In the final state, the 100-kg clown is moving with a speed of 15 m/s. And the 500-kg cannon moves in the opposite direction of the clown (which is consistent with the term 'recoil speed') with a speed of V.

Thus, ∑p_f = ( 100 ) ( 15 ) - ( 500 ) V = 1500 - 500 V

Using the conservation of momentum:

0 = 1500 - 500 V ⇒ 500 V = 1500 V = 3 m/s

I hope this helps! Message me in the comment section if there is anything confusing about my explanation or if I made a mistake!