(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A spaceship of mass M is traveling in deep space with velocityv_{i}= 20 km/s relative to the Sun. It ejects a rear stage of mass 0.2 M with a relative speedu= 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 andv_{f}be the velocity of the ship after ejection.

3. The attempt at a solution

p_{i}= Mv_{i}

p_{f}= 0.2MU + 0.8Mv_{f}

it's an example from the book and the next thing they do is say "The speeduof the ejected stage relative to the spaceship is the difference in velocities of the spaceship and stage"

u=v_{f}- U

or

U =v_{f}-u

basically, I am feeling really dumb for not understanding whyu=v_{f}- U. The example also states that the positive direction is in the direction ofv_{i}. If that's so, then shouldn'tube negative? I think I'm thinking about this too hard and have confused myself.

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# Homework Help: Simple Vector Question Related to Conservation of Momentum

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