Question

The expanding gases that leave the muzzle of a rifle also contribute to the recoil. A 30-caliber bullet has a mass 0.00720 𝑘𝑔 and a speed of 601 𝑚/𝑠 relative to the muzzle when fired from a rifle that has a mass of 2.80 𝑘𝑔. The loosely held rifle recoils at a speed of 1.85 𝑚/𝑠 relative to the earth. Find the momentum of the propellant gases in a coordinate system attached to the earth as they leave the muzzle of the rifle.

Answer 1

By momentum conservation:

$$m_bv_b+p_g=m_rv_r,\\ p_g=m_rv_r-m_bv_b=0.853\text{ kg}·\text{m/s}.$$