# Launch speed of the package?

1. Jan 2, 2010

### D. Tran

1. The problem statement, all variables and given/known data

A spaceship is coasting with a constant velocity of 124 m/s. The ship fires a deep space "care package" of mass 1300 kg. The firing of the care package brings the rocket ship to a halt. If the mass of the spaceship, not including the rocket, is 4.0 x 106 kg, what is the launch speed of the package?

2. Relevant equations

p=mv
ΣPi=ΣPf

PiS=msvs
PiP=mpvp
PfS=msvs
PfP=msvs

ΣPi=PiS+PiP
ΣPf=PfS+PfP

final equation: mSviS+mPviP=mSvfS+mPvfP

where s=spaceship and p=package

3. The attempt at a solution

mS=4.0 x 106 kg
viS=124 m/s
vfS=0
mP=1300 kg
viP=?
vfP=?

I do not know if the final equation used is correctly applied. After plugging in all of the known variables, there are two unknown. Could someone point me in the general direction?

Thank you for your time and help.

-D. Tran

2. Jan 2, 2010

### pgardn

Re: Momentum.

The initial momentum could be written as (mass of package + mass of spaceship)v. The package and space ship are moving as one to begin with, yes?

All of the above are known.

the final momentum (after the firing or impulse) can be written as you have it and all of the variables are known except the velocity of the package. Which you should now be able to find.

3. Jan 2, 2010

### D. Tran

Re: Momentum.

Is finding the initial velocity of the package the same as finding the launch speed?

4. Jan 2, 2010

### PhanthomJay

Re: Momentum.

As pgardn has noted, the initial velocity of the spaceship, and the initial velocity of the package, are, with respect to a third party observer, the same. The launch speed is the final velocity of the package v_f (its velocity after it has been fired).