1. The problem statement, all variables and given/known data A spaceship of mass M is traveling in deep space with velocity vi = 20 km/s relative to the Sun. It ejects a rear stage of mass 0.2 M with a relative speed u = 5 km/s. What then is the velocity of the spaceship? 2. Relevant equations conservation of momentum, p = mv let U be the velocity of the ejected rear stage and vf be the velocity of the ship after ejection. 3. The attempt at a solution pi = Mvi pf = 0.2MU + 0.8Mvf it's an example from the book and the next thing they do is say "The speed u of the ejected stage relative to the spaceship is the difference in velocities of the spaceship and stage" u = vf - U or U = vf - u basically, I am feeling really dumb for not understanding why u = vf - U. The example also states that the positive direction is in the direction of vi. If that's so, then shouldn't ube negative? I think I'm thinking about this too hard and have confused myself.