Classical Mechanics: linear resistance

Jumblebee
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Homework Statement


Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*vext+Fext show that if the rocket starts from rest and efects mass at a constant rate k= -m' then its speed is given by v=(k/b)vex[1-(m/m0)^b/k]

The Attempt at a Solution


so i thought maybe I was suppose to integrate both sides of the equation
mv'= -m'*vext+Fext, but then i really didn't know where to go from there. Any help?
 
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I think your missing piece of information is to realize that the mass of the rocket depends on time:

m(t) = m_0 - kt
 
Do I not need to integrate then? I just don't know where the power of b/k comes from.
 
You still need to integrate, but the integral is different.
 
I still can't get this one to work out. Am I still missing information? I tried starting with the equation mv'= -m'*vext+Fext. I solved for v'. and then substituted in the equation m0-kt. But then I didn't know where to go from there.
 
help, I'm still stuck, can anyone help me?
 

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