(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A rocket that starts at rest with mass M ejects exhaust at a given speed u. what is the mass of the rocket(including unused fuel) when its momentum is maximum?

2. Relevant equations

p=mv

3. The attempt at a solution

well basically i used conservation of momentum to get the velocity of the rocket with respect to mass. after doing all the integrating work i got v=uln(M/m) assuming that m is the mass of the rocket at a later time. plugging the velocity into the p=mv formula i differentiate with respect to mass where the equation becomes dp/dm=u[ln(M/m)-1/m^2]. now i set dp/dm to zero to try to find the mass needed for a max momentum but unfortunately the dp/dm equation isn't easy to solve due to the "ln" function. Am i doing something wrong here?

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# Homework Help: Rocket momentum question.

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