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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.