[problem] State the fundemental equation of motion for a particle of variable mass. A rocket of initial mass m0 is fired vertically, under the influence of a uniform gravitational field, and expels propellant at a constant relative velocity c downwards. The propellant is completely consumed after a time T, leaving the rocket with a mass mT. Calculate the velocity and position at time t < T. Show that the velocity at time T is independent of the rate of consuming the propellant. [/problem] I don't know how to go about solving this. I vaguely recall the principle behind rocket flight; the reaction force against the expulsion of propellant is what drive the rocket upwards. The resultant force will be something like F = f(c) - mg, m of course being a variable and f being some function of c. I have no worked examples for this type of problem to refer to, so I need someone to show me the steps involved.