# Linear Momentum - Module and Shuttle Go Boom

1. Nov 11, 2009

### Flamefury

1. The problem statement, all variables and given/known data
A 500.0 kg module is attached to a 400.0 kg shuttle craft, which moves at 1000 m/s relative to the stationary main spaceship. Then a small explosion sends the module backward with speed 100.0 m/s relative to the new spaeed of the shuttle craft. As measured by someone on the main spaceship, by what fraction did the kinetic energy of the module and shuttle craft increase because of the explosion?

2. Relevant equations
I treated this question as an inelastic collision, so I have no idea if I'm even using the right equations...Nevertheless.
m1v1i + m2v2i = m1v1f + m2v2f
KE = (mv2) / 2

3. The attempt at a solution
m1 = 400 kg
m2 = 500 kg
m1i = m2i = 1000 m/s
m2f = m1f - 100 m/s

Using the momentum equation, I isolate for m1f and get 1055.55556 m/s. Therefore, m2f = 955.55556 m/s.

Then I calculate the KE after the explosion by adding together the KE of the shuttle and the KE of the module, and divide that sum by 0.5*900 kg*(1000 m/s)^2.

My answer came out as an increase of 0.247%. I have no idea if this is right, because there's no answer key. But I don't feel too confident about the steps I took to reach the answer.