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First order nonlinear ode

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    We recently discussed a problem in class involving free fall and parachutes.One of the examples was to solve for the area of a parachute in drag,gravity,air density,mass and the speed at which the object deployed the parachute and the speed it hit the ground out. I'm pretty sure I know how to do the porlbem if I could only get past the first few steps. My guess is that I need to solve the following nonlinear ode:

    m (dV/dt) = mg-(1/2)(air density)(drag constant)(area parachute)(V)^2
    i replaced the equation with something like this to simplify it:
    m (dV/dt) = mg-kV^2 where k is all those constants

    now i'm familiar with seperable ode's and this is the form i obtained:
    dV/dt = g-(k/m)V^2

    from then on i am lost, i think i just need a bit of help onto the next step or two then i should be able to get the problem rolling. Any help or input would be greatly appreciated! Thank you.
     
  2. jcsd
  3. Mar 26, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi francisg3! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    yes, so dV/(g-(k/m)V2) = dt :wink:
     
  4. Mar 26, 2009 #3

    HallsofIvy

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    And you can use partial fractions to integrate that.
     
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