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Classical Mech - Newtons 2nd. Quad Air Resistance

  1. Sep 9, 2014 #1
    1. The problem statement, all variables and given/known data

    A puck of mass m is kicked up an incline (angle θ) with initial speed vo. Friction is not present, but air resistance has a magnitude of f(v) = cv2. Solve Newtons second law for the pucks velocity as a function of t on the upward journey. How long does the journey last?

    2. Relevant equations


    3. The attempt at a solution

    mr'' = -mgsinθ - fquad

    mv' = -mgsinθ - cv2 v(hat)

    dv/dt = -gsinθ -(c/m)v2 v(hat)

    dt = -dv/ (gsin θ -(c/m)v2 v(hat) )


    I'm not quite sure how to solve this; perhaps I could rewrite to get a known integral of 1/(1 +x^2) dx, but I don't see how.
     
  2. jcsd
  3. Sep 10, 2014 #2

    haruspex

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    You can drop the v(hat), since you've reduced it to scalars, all motion being in the one dimension.
    Can you do it from there?
     
  4. Sep 10, 2014 #3
    I don't think so. Should I just rewrite it as:

    dt = -(gsin θ -(c/m)v^2)^-1 dv and integrate?
     
  5. Sep 11, 2014 #4

    haruspex

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    Yes, except that you just made a sign error.
     
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