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DE Derivative Using Euler's Method

  1. Feb 17, 2013 #1
    1. The problem statement, all variables and given/known data

    The velocity v of a skydiver is well modeled by a differential equation:

    m*dv/dt = mg - k*v^2

    Where m is the mass of the skydiver, g = 9.8 m/s^2 is the gravitational constant, a k is the drag coefficent determined by the position of the diver during the dive. Consider a diver of mass m = 54 kg with a drag coefficient of 0.18 kg/m. Use Euler's method to determine how long it will take the diver to reach 95% of her terminal velocity after she jumps from the plane.


    2. Relevant equations

    Euler's method:
    y[k+1] = y[k] + f(t[k],y[k])*DeltaT



    3. The attempt at a solution

    I placed the constants into the equation to get:
    dv/dt = (529.2 - 0.18*v^2) / 54

    Then, using Euler's method with a very small delta T, I find terminal velocity to be 54.2218. This would mean that the diver reaches 95% of terminal velocity at approximately 51.5107.

    1) Is this the correct way of approaching the problem? Is my terminal velocity correct?
    2) From here I suppose I would just find the point where y[n] = 51.5107?

    If anyone can help me I would greatly appreciate it!
     
  2. jcsd
  3. Feb 17, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    Sure, terminal velocity is where dv/dt=0. You don't even need the numerical solution to find the terminal velocity. So that part looks ok, and yes, find where y[n] = 51.51.
     
    Last edited: Feb 17, 2013
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