With the engines off, a spaceship is coasting at a velocity of +210 m/s through outer space. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1350 kg, and the mass of the spaceship (not including the rocket) is 2.5 106 kg. The firing of the rocket brings the spaceship to a halt. What is the velocity of the rocket?

Question

With the engines off, a spaceship is coasting at a velocity of +210 m/s through outer space. It fires a rocket straight ahead at an enemy vessel. The mass of the rocket is 1350 kg, and the mass of the spaceship (not including the rocket) is 2.5  106 kg. The firing of the rocket brings the spaceship to a halt. What is the velocity of the rocket?

drwls · Accepted Answer

The rocket acquires all of the original momentum of the spaceship stops.
(M + m)V1 = m V2
2.5*10^6* 210 = 1350*V2
V2 = 3.89*10^5 m/s
This is an unrealistically high velocity for a rocket, or even a bullet-fired projectile. Furthermore, the spaceship fired a real rocket, most of the velcoty of the rocket would be acquired after release, and would not affect the velocity of the spacecraft. In that case, momentum conservation could not be used.