How Long to Reach 90% Terminal Velocity for a Ping Pong Ball?

[pimpalicous]

Homework Statement

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

Homework Equations

Fd=1/2*C$$_{w}$$+$$\rho$$*A*v^2

Newton's second law

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.