Recoil of the cannon

Problem

A $500$ kg cannon, at rest, fires a $4{,}0$ kg projectile with velocity $10$ m/s. Calculate the recoil velocity of the cannon (isolated system along the firing axis).

Solution

The cannon + projectile system is isolated along the firing axis: total momentum is conserved. Before firing everything is at rest, so the initial momentum is zero (it is an explosion). $p_\text{iniziale} = 0 = m_c v_c + m_p v_p$ I find the cannon’s velocity $v_c$: $v_c = -\frac{m_p v_p}{m_c} = -\frac{4{,}0 \cdot 10}{500} = -\frac{40}{500} = -0{,}080\ \mathrm{m/s}$ The minus sign indicates that the cannon recoils in the direction opposite to the projectile.

Final result: $\ev{v_c = -0{,}080\ \mathrm{m/s}\ \text{(recoil)}}$

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Topics: Quantità di moto e urti Concepts: Conservazione della quantità di moto · Esplosione Skills: Conservazione della quantità di moto