Question

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s^-1, what is the recoil speed of the gun?

Answer 1

Given: m₁ = 0.02 kg, m₂ = 100 kg, v₁ = 80 m s^-1

To find: Recoil speed (v₂)

Formula: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Calculation: Initially gun and shell are at rest.

∴ m₁u₁ + m₂u₂ = 0

Final momentum = m₁v₁ – m₂v₂

Using formula,

0 = 0.02 (80) – 100(v₂)

∴ v₂ = \(\frac{0.02\times80}{100}\) = 0.016 ms^-1

The recoil speed of the gun is 0.016 m s^-1.