Drag force/difficult integral.

[pimpalicous]

1. The problem statement, all variables and given/known data
If a ping pong ball is released from rest, how long does it take for the ping pong ball to reach 90% of its terminal velocity?

m=2.2g, density(air)=a.29kg/m^3, Cw=.5, diameter=.38mm


2. Relevant equations
Fd=1/2*C_{w}+\rho*A*v^2

newton's second law



3. The attempt at a solution

I set up newtons second law for the going down case. I wanted to get v in terms of t.
I can't solve the integral though.

Fd-mg=m*dv/dt

\int \frac{dt}{m}=\int \frac{2*dv}{C_{w}*\rho*A*v^2-mg}

Please help.

[CompuChip]

Maybe you can use
\frac{\mathrm d}{\mathrm dx} \operatorname{arctanh}(x) = \frac{1}{1 - x^2}

[pimpalicous]

yeah, i was able to get it to that form and it worked. Thanks.