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?