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Homework Help: Differential Equations KE Problem

  1. Mar 19, 2010 #1
    1. The problem statement, all variables and given/known data

    We're supposed to find the object's KE and heat. Given:

    Forces on Object: Air Drag + Gravity
    Air Drag = .5(coefficient of drag)(1.2 kg/m3)v2A
    A = cross sectional area
    R = Radius of object
    Object is X Km above the ground
    Initial velocity = V

    We are told it should be an initial value problem.

    2. Relevant equations

    Possibly y"+ (Force due to Drag)y' + (gravity)y = 0

    3. The attempt at a solution

    I tried plugging in the initial conditions to the equation above, but I'm stuck at that point.
     
  2. jcsd
  3. Mar 20, 2010 #2
    How did you get that equation?

    Since kinetic energy has nothing to do (directly) with position, you shouldn't have to solve for y (which I'm assuming stands for the height of the object); instead, focus on v(t), and don't forget that a(t) = dv/dt
     
  4. Mar 20, 2010 #3
    I just sort of assumed that's the equation we had to use, but I wasn't sure?

    What initial value differential equation should I be using?
     
  5. Mar 20, 2010 #4
    You should be able to derive an equation using newton's second law and what you know about the forces acting on the object
     
  6. Mar 20, 2010 #5
    I was originally going to do it entirely with Newton's laws, but I'm having a hard time seeing how Newton's equations can "convert" into DE?
     
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