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?
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.
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
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.