Answer to Question #299712 in Physics for Phil

Question

A cannon is mounted on a railroad car. The cannon fires a 1.75kg ball with a muzzle velocity 300.m/s to the left. The mass of the cannon-car combo is 4500.kg. if all is initially at rest, what is the recoil velocity of the cannon-car?

Answer 1

Given:

$m_{cannon}=4500\:\rm kg$

$m_{ball}=1.75\:\rm kg$

$v_{ball}=300\:\rm m/s$

The law of conservation of momentum says

$$m_{ball}v_{ball}=m_{cannon}v_{cannon}$$

Hence, the recoil speed of the gun

$$v_{cannon}=\frac{m_{ball}v_{ball}}{m_{cannon}}=\frac{1.75*300}{4500}=0.12\:\rm m/s$$