Optimizing Rocket Momentum: Finding the Maximum Point

[wltrtn]

Homework Statement

The mass of a rocket as it burns its fuel is constantly decreasing, while its speed is increasing. We want to know when the momentum is at its maximum. At what fraction of the initial mass is the momentum a maximum?

Homework Equations

P = mv

The Attempt at a Solution

I'm guessing I have to relate velocity to mass somehow so I can get an equation of momentum that is dependent on mass. Then I find when dP/dm = 0.

 

[CWatters]

Perhaps assume that rocket produces constant thrust F (probably not correct) and the mass decreases uniformly with time. Then write an equation for the acceleration using F = ma where both m and a will be a function of time?