# Multistage Rocket

1. Oct 24, 2009

### GB89

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

I need to find the final velocity of a multistage rocket (accelerating from rest in free space) that burns its fuel in two stages. In the first stage, it burns 3/10 of its initial mass as fuel. Then it jettisons its first-stage fuel tank, which has a mass of 1/10 the initial mass of the rocket. Then, it burns 3/10 of its initial mass as fuel.

2. Relevant equations

I think that the equation is:

Final Velocity = V(exhaust) times ln(m0/m) + V(exhaust) times ln(m0/m).

3. The attempt at a solution

Is the m0 in the second part of the equation 6/10 initial mass, or 9/10 initial mass (does the fuel burned in the first stage get subtracted too)?

I think the answer is V(exhaust) times ln(1/.7) + V(exhaust) times ln(.6/.3), giving a final answer of 1.0498 times the exhaust velocity. Is this correct?

EDIT: PLEASE DISREGARD. I just noticed that this question was answered in a "Similar Thread." My appologies.

Last edited: Oct 24, 2009