- #1

happyparticle

- 410

- 20

- Homework Statement
- quadratic and linear air resistance

- Relevant Equations
- f = ma

f = -bv -cv²

Hi,

I'm trying to solve this integral and then isolate V, but I can't get the right answer. I don't know where is my errors. I probably muffed the integral.

##-bv -cv² = m\frac {dv}{dt}##

##

\int_0^t dt = - m \int_{Vo}^v \frac {dv}{bv+cv^2}

##

I get this after the integration

##t = -m[ln\frac{V}{Vo} - \frac cb ln(\frac {b+cV}{b+cVo})]##

Finally, I get

##

v = \frac{e^{\frac{-bt}{cm}} VoB}{b +cVo- e^{\frac{-bt}{cm}}VoC}

##

But the right answer is

##

v = \frac{b +cVo}{b +cVo- e^{\frac{-bt}{m}}VoC} -1

##

I'm trying to solve this integral and then isolate V, but I can't get the right answer. I don't know where is my errors. I probably muffed the integral.

##-bv -cv² = m\frac {dv}{dt}##

##

\int_0^t dt = - m \int_{Vo}^v \frac {dv}{bv+cv^2}

##

I get this after the integration

##t = -m[ln\frac{V}{Vo} - \frac cb ln(\frac {b+cV}{b+cVo})]##

Finally, I get

##

v = \frac{e^{\frac{-bt}{cm}} VoB}{b +cVo- e^{\frac{-bt}{cm}}VoC}

##

But the right answer is

##

v = \frac{b +cVo}{b +cVo- e^{\frac{-bt}{m}}VoC} -1

##