Find the gain in kinetic energy when a rocket emits a small amount of matter. (Well, there's more, but the rest of the question is built around this initial problem)...
The Attempt at a Solution
My logic revolves around the total kinetic energy of the rocket after ejecting matter, which I took to be the kinetic energy before the emission added to the gain in kinetic energy. Furthermore, the mass of a rocket emitting a small amount of matter is reduced by dM = -dm and its velocity increases wth dv to (v+dv). If we let u = velocity at which matter is ejected, then after combining all of the above into a single equation we have:
But this doesn't seem to be leading in the right direction and I personally believe there is a flaw in my reasoning.
So how am I supposed to set up this problem?