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 Data

• Shell mass: \(m_s = 0.020\) kg
• Gun mass: \(m_g = 100\) kg
• Muzzle speed: \(v_s = 80\) m/s
• Initial: both at rest

Shell →→→ 80 m/s
GUN ←←← ???

Conservation of Momentum

System isolated horizontally. Total momentum conserved:

$$p_\text{initial} = p_\text{final}$$ $$0 = m_s v_s + m_g (-v_g)$$ $$m_g v_g = m_s v_s$$ $$v_g = \frac{m_s v_s}{m_g}$$

Calculation

$$v_g = \frac{0.020 \times 80}{100} = \frac{1.6}{100} = 0.016 \, \text{m/s}$$

Recoil Speed of Gun

\(v_g = \textbf{0.016 m/s}\) (or 1.6 cm/s backward)

Verification

Object	Mass (kg)	Velocity (m/s)	Momentum (kg·m/s)
Shell	0.020	+80	+1.60
Gun	100	-0.016	-1.60
Total	-	-	0 ✓

Physical Insight

• Mass ratio 5000:1 → velocity ratio 1:5000
• Recoil barely noticeable (person holding gun absorbs it)
• Real guns have barrel + person mass → even less recoil