Question

a gun of mass m kg fires a shell of mass 1.5 kg with a velocity of 150 m/s. and recoils with a velocity of 1.5 m/s. calculate the mass of the gun.

Answer 1

Mass of shell is, m_s = 1.5 kg

Velocity of the shell, v_s = 150 m/s

Mass of gun = m

Recoil velocity of the gun is = -1.5 m/s [we include the negative sign because velocity of gun is opposite to the velocity of the shell]

Now, momentum of the system before firing = 0 [since all were at rest]

Momentum of the system after firing = (1.5)(150) + (m)(-1.5) = 225 – 1.5m

By law of conservation of momentum,

225 – 1.5m = 0

=> m = 150 kg