- #1

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## Homework Statement

A spaceship of mass M is traveling in deep space with velocity

*v*

_{i}= 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?

## Homework Equations

conservation of momentum, p = mv

let U be the velocity of the ejected rear stage and

*v*

_{f}be the velocity of the ship after ejection.

## The Attempt at a Solution

p

_{i}= M

*v*

_{i}

p

_{f}= 0.2MU + 0.8M

*v*

_{f}

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*=

*v*

_{f}- U

or

U =

*v*

_{f}-

*u*

basically, I am feeling really dumb for not understanding why

*u*=

*v*

_{f}- U. The example also states that the positive direction is in the direction of

*v*

_{i}. If that's so, then shouldn't

*u*be negative? I think I'm thinking about this too hard and have confused myself.