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Air resistance and velocity

  1. Jan 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Given: effects of drag for a free falling body are a= 9.81[1-(v^2)*10^-4] m/s^2
    V0 = 0 m/s and the falling body is very very high

    Find: the velocity after 5 seconds and the bodies terminal velocity as t -> infinity


    2. Relevant equations

    ∫dv = ∫a dt

    3. The attempt at a solution

    ∫ 1/(1-(v^2)*10^(-4)) dv = ∫ 9.81 dt where t goes from 0 to 5

    When I integrate this I get

    5*10^(-4) * ln( abs( v+1) / abs( v -1)) - 5*10^(-4) * ln( abs(1) / abs( 1)) = 9.81 m/s^2 * 5s

    For some reason I don't think this is right and if it is how do you solve it?

    thanks
     
  2. jcsd
  3. Jan 18, 2013 #2

    haruspex

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    You have dv/dt = 9.81[1-(v^2)*10^-4].
    Can you rearrange that as t = ∫ f(v) dv?
     
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