Drag force/difficult integral.

1. Sep 3, 2008

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

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

2. Sep 4, 2008

CompuChip

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

3. Sep 4, 2008

pimpalicous

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