A 1900-kg cannon shoots a 5-kg cannon ball at a velocity of 25 m/s.What is the recoil velocity of the cannon?
A)0.033 m/s
B)0.066 m/s
C)0.132 m/s
D)0 m/s
E)1.23 m/s

Question

Quizplus · Accepted Answer

This problem can be solved using conservation of momentum. The initial momentum of the system (cannon + cannonball) is 1900 kg × 0 m/s (since the cannon is initially at rest) + 5 kg × 25 m/s = 125000 kg·m/s. After the cannonball is fired, the final momentum of the system is (1900 kg + 5 kg) × v, where v is the recoil velocity of the cannon. By setting the initial and final momenta equal, we can solve for v:

1900 kg × 0 m/s + 5 kg × 25 m/s = (1900 kg + 5 kg) × v

125000 kg·m/s = 1905 kg × v

v ≈ 65.55 m/s

However, we are asked for the recoil velocity of the cannon, which is the opposite direction of the cannonball's velocity. Therefore, the recoil velocity of the cannon is -65.55 m/s, which rounded to two decimal places is -0.07 m/s or -0.066 m/s (since we are not given the direction, the answer should be given with a positive value). Therefore, the best choice is B.

A 1900-Kg Cannon Shoots a 5-Kg Cannon Ball at a Velocity