# Classical Mechanics: linear resistance

1. Dec 7, 2008

### Jumblebee

1. The problem statement, all variables and given/known data
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]

3. 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?

2. Dec 7, 2008

### Irid

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

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

3. Dec 7, 2008

### Jumblebee

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

4. Dec 8, 2008

### Irid

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

5. Dec 8, 2008

### Jumblebee

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.

6. Dec 8, 2008

### Jumblebee

help, I'm still stuck, can any one help me?