Optimizing Rocket Momentum: Finding the Maximum Point

AI Thread Summary
To determine when a rocket's momentum is at its maximum, the relationship between mass and velocity must be established, as momentum (P) is defined as P = mv. The discussion suggests deriving a momentum equation dependent on mass and finding the point where the derivative of momentum with respect to mass equals zero (dP/dm = 0). It is proposed to assume constant thrust and uniform mass decrease over time, leading to the need for an equation that incorporates both mass and acceleration as functions of time. This approach aims to optimize the rocket's momentum by analyzing the interplay between decreasing mass and increasing velocity. Understanding these dynamics is crucial for identifying the fraction of initial mass at which momentum peaks.
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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.
 
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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?
 
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