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Help with diffy eqn terminal vel problem

  1. Jan 10, 2006 #1

    So m*dv/dt = mg - kv^2, where m is skydiver mass, g acceleration due to gravity, and k> 0 related to amount of air resistance. So I want to find the analytical solution for v(t), with the assumption that v(0) = 0.

    I went all the way to integrating it with a partial fraction, but then got an answer drastically different from what the book got.

  2. jcsd
  3. Jan 10, 2006 #2


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    It's hard to answer because you didn't show us what you did or what answer you got!
  4. Jan 11, 2006 #3


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    Tell you what Ara, how about looking up Riccati equations. Now, can your equation be put in such form? If if can, then such a prespective may allow an easier approach to its solution.
  5. Jan 11, 2006 #4


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    Dearly Missed

    Please remember that the inverse of the hyperbolic tangent is a logarithmic expression.
  6. Jan 11, 2006 #5
    If you just want the terminal velocity then set the acceleration (LHS) equal to zero and solve for v. I did a question like this about 1 or 2 years ago. If I remember correctly, the working is a little tedious but not too difficult. Obtaining the partial fraction decomposition is the difficult part, the integration and transposition should be straight forward.
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