Classical Mechanics: linear resistance

[Jumblebee]

Homework Statement

Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*v_ext+F^ext 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)v_ex[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'*v_ext+F^ext, but then i really didn't know where to go from there. Any help?

 

[Irid]

I think your missing piece of information is to realize that the mass of the rocket depends on time:

$$m(t) = m_0 - kt$$

 

[Jumblebee]

Do I not need to integrate then? I just don't know where the power of b/k comes from.

 

[Irid]

You still need to integrate, but the integral is different.

 

[Jumblebee]

I still can't get this one to work out. Am I still missing information? I tried starting with the equation mv'= -m'*v_ext+F^ext. I solved for v'. and then substituted in the equation m₀-kt. But then I didn't know where to go from there.

 

[Jumblebee]

help, I'm still stuck, can anyone help me?