A gun is mounted on a railroad car. The combined mass of the car, the gun, the shells, and the operator is 50m , where m represents the mass of a single shell. If the shell's velocity relative to the gun (in its state prior to firing) is 200 m/s , determine the recoil speed of the car following the second shot. Neglect friction.

Step-by-step solution

Let the initial mass of the system be M₀ = 50m and the velocity of the shell relative to the gun prior to firing be u = 200 m/s . For the first shot, the initial momentum of the system is zero. Since the gun is initially at rest, the velocity of the first shell relative to the ground is u . The mass of the remaining system (car, gun, operator, and remaining shells) is 49m . Let V₁ be the velocity of the car after the first shot. By conservation of linear momentum: 0 = 49m V₁ + m u V₁ = - u 49 For the second shot, t