A gun of mass 3kg fires a bullet of mass 30g. The bullet takes 0.003s to move through the barrel of the gun and acquires a velocity of 100 m/s. Calculate:

**a)** The velocity with which the gun recoils

**b)** The force exerted on the gunman due to the recoil of the gun

Answer:

Mass of the gun, m1 = 3kg

Mass of bullet, m2 = 30g = 0.03kg

Velocity of bullet, v2 = 100 m/s

**a)** According to conservation of momentum

m1v1 = m2v2

v1 = 1 m/s

**b)** Initial velocity of the gun, u = 0 m/s

Final velocity of the gun, v = 1 m/s

Time, t = 0.003s

Acceleration, a = (u-v)/t = 1000/3 \mathrm{m/ s^2}

Force = ma = 1000N

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