Question

2)A shell of mass 3kg is fired from a gun with a velocity of 200 m/s. Knowing that the gun is free to move and its mass of 1400 kg,calculate its recoil velocity after firing the shell.

Answer 1

Question 36813

Let us denote $m_{s} = 3kg$ , $v_{s}' = 200\frac{m}{s}$ , $m_{g} = 1400kg$ . Index "s" means shell and "g" means gun.

In order to find recoil velocity, one has to use the law of conservation of linear momentum:

$m_{s}v_{s} + m_{g}v_{g} = m_{s}v_{s}' + m_{g}v_{g}'$ . Before firing the shell all velocities were zero, hence

$0 = m_{s}v_{s}^{\prime} + m_{g}v_{g}^{\prime}$ , from here we get $v_{g}^{\prime} = \frac{-m_{s}v_{s}^{\prime}}{m_{g}}\approx -0.43\frac{m}{s}$ - this is the recoil velocity of the gun.