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## Homework Statement

OK, this seems simple but I want to make sure I am not doing something totally wrong. The problem says: use the conservation of mass of a system of many particles to shoe that the thrust force of a rocket that ejects mass at rate [itex]\frac{dm}{dt}[/itex] is equal to [tex]F=-v_e \frac{dm}{dt}[/tex] where [itex]v_e[/itex] is the velocity of the mass ejected.

## The Attempt at a Solution

I looked at it this way: momentum is conserved so if we start with mass m of the rocket, mv = k (where k is a constant).

SInce we have a simple differential equation [itex]F=-v_e \frac{dm}{dt}[/itex] it can be integrated as [itex]-m v_e = Ft[/itex]. Taking the derivative w/r/t time we get [itex]-m \frac {d v_e}{dt} = F[/itex]

That gets us the F=ma part of the equation, showing that that works. But I notice that if momentum is a k (constant) then [itex]-m v_e = k = Ft[/itex].

There's a step I am missing here I think. I feel like I am almost there. Any hep -- and anyone telling me I have approached this in entirely the wrong way -- would be appreciated.