# Momentum Principle question dealing with a spacecraft's velocity

## Homework Statement

You are navigating a spacecraft in space. The mass of the spacecraft is 4.0 x 10^4 kg. The engines are off, and you're coasting with a constant velocity of ‹ 0, 28, 0 › km/s. As you pass the location ‹ 5, 6, 0 › km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of ‹ 5.0 105, 0, 0 › N for 22 s. The gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the engines turned off. Where are you an hour later?

## Homework Equations

Instructions say to use the step one of the Momentum Principle (p = Fnet(Δt)), then step one of the position update equation. I'm not sure if I am using the right equation, I think it's →rf = →ri + Vavg(Δt). I have also used pf = pi + Fnet(Δt), rf = ri + viΔt + 1/2(F/m)(Δt^2).

## The Attempt at a Solution

Well, when I first attempted the question, I used the Momentum Principle to find the initial momentum. After finding the initial momentum, I found the final momentum using the equation pf = pi + Fnet(Δt). I then found the final velocity by rearranging p = mv... then got stuck. I attempted to use rf = ri + viΔt + 1/2(F/m)(Δt^2), but that didn't result in a correct answer. I'm not sure if I'm misunderstanding the question, or the instructions.
Help is very much appreciated! Thank you so much.

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Simon Bridge