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I need some guidance in this problem. Consider a rocket taking off vertically from rest in a gravitational field g, the equation of motion (which I had to derive in the previous part of this problem) is:

[tex]

m \dot{v} = -\dot{m}v_{ex} - mg

[/tex]

where

m is the mass of the rocket

[tex] v_{ex} [/tex] is the the speed at which the exhaust fuel is being ejected relative to the rocket

Also, assume that the rocket is ejecting mass at a constant rate, so [tex] \dot{m}=-k [/tex] (where k is a positive constant) so that [tex]m = m_{0} - kt [/tex]

Solve the equation for v as a function of t, using separation of variables (rewriting the equation so that all the terms involving v are on the left and all the terms involving t on the right)

Now what is confusing me is at what point to I have to substitute for

[tex] \dot{m} [/tex] and m ?

Can I start by saying, [tex] m \frac{dv}{dt} = k v_{ex} - mg [/tex]

and then plug in [tex] m = m_{0} - kt [/tex] and take it from here?

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# Homework Help: Separation of variables problem

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