1. The problem statement, all variables and given/known data Rocket launched runs out of fuel after accelerating "for a short distance," coasts to a maximum altitude, then falls back. Known: rocket mass, max. altitude, g. Find velocity when rocket runs out of fuel. 2. Relevant equations There doesn't seem to be enough information to use kinematic eqs: no time for anything, no initial acceleration; only maximum height. We know the rocket force must be at least mg, but it's clearly more, since it coasts upwards. 3. The attempt at a solution Seems to need energy methods, but I can't see the way. E=K+U, but E=U (at top) doesn't equal E at bottom, where K and U are both zero. And what can we know about K+U at yfuelanyway? Do I need work, force? Do I need Wnonconservative=∆K+∆U? Does momentum enter this? I know that force changes from rocket to gravity at yfuel, but I'm not sure what to do with that. I could use a shove in the right direction. If I try K1+U1=K2+U2 at y1=no fuel and y2=max. altitude, I just wind up with v2=2g(y2-y1), the kinematic eq., and I have two unknowns. I need another expression with one of these variables in it. Momentum? Kinematics? Thanks.