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## Homework Statement

A rocket in free space that starts at rest with total mass M ejects exhaust gas at a given speed u. What is the mass of the rocket(including unused fuel) when its momentum is maximum? What is the mass when its energy is maximum? [use E=.5mv^2 for energy]

## Homework Equations

Mv=P

E=.5mv

^{2}

v=v0+uln(m0/m) (maybe?)

## The Attempt at a Solution

Mv=0

-m

_{exhaust}u+(M-m

_{exhaust})v=0

(M-m

_{exhaust})v=m

_{exhaust}u

v=(m

_{exhaust}/(M-m

_{exhaust}))u

I'm stuck here. Do I take the derivative of v?