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Homework Help: Drag force/difficult integral.

  1. Sep 3, 2008 #1
    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

    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.


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

    Please help.
  2. jcsd
  3. Sep 4, 2008 #2


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    Science Advisor
    Homework Helper

    Maybe you can use
    [tex]\frac{\mathrm d}{\mathrm dx} \operatorname{arctanh}(x) = \frac{1}{1 - x^2}[/tex]
  4. Sep 4, 2008 #3
    yeah, i was able to get it to that form and it worked. Thanks.
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