A space vehicle is traveling at 4100 km/h relative to Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 76 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (in km/h) of the command module relative to Earth just after the separation?

Answer 1

Try applying the law of conservation of momentum in the coordinate sytem of the Earth. The momentum lost by the ejection of the motor must equal the momentum gained by the remaining command module. This assumes that the ejection occured due to a "push" of some kind from the command module -- not a rocket motor retrofiring after separation.