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Drag forces

  1. Jan 18, 2012 #1
    If I wanted to make a graph of height versus time for an object under the effects of air resistance av+bv^2 and thrown with a given initial speed, how would I go about doing that? I was also hoping to get a y versus x graph for a projectile under the same drag, but I presume I could find x versus t the same way I end up finding y versus t and then treating the two like a parameterized curve.

    I thought about using ma = av+bv^2-mg and taking the integral twice to get height as a function of time, but my limited calculus skills are failing at that. Even simplifying to just bv^2 seems to be too much for me. Is this the best way to do it? Is there a numerical way to do it? (I've never done integrals numerically on a computer or anything)

    In general, I don't really know how to tackle these kinds of messy integrals. Are there any resources I could learn from?

    Thanks.
     
  2. jcsd
  3. Jan 18, 2012 #2

    Simon Bridge

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    mdv/dt = av+bv^2 - mg

    so:[tex]\int \frac{mdv}{av+bv^2-mg} = \int dt[/tex]... then find the constant of integration from the fact that v(0)=u.

    http://www.jstor.org/pss/2372332
     
    Last edited: Jan 18, 2012
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