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Homework Help: Effects of drag on the distance of a car travelling

  1. Apr 1, 2010 #1
    1. The problem statement, all variables and given/known data
    A car starts at 100 m/s and deploys a parachute. After 10 seconds its speed decreases to 45.45 m/s. Calculate the distance the car has travelled in this duration. The effects of ground resistance are ignored.

    drag coefficient and planform area product (Cd * A) = 4 m^2


    2. Relevant equations

    drag force, Fd = 1/2 (rho) * u^2 * Cd * A

    rho = density, 1.22 kg/m^3
    u = speed
    Cd = drag coefficient
    A = planform area

    -Fd = m du/dt

    m = mass



    3. The attempt at a solution

    Basically I managed to calculate the speed after 10 seconds which is 45.45 m/s by integrating -Fd = m du/dt.

    I cannot use the SUVAT equations to calculate the distance because it is not constant acceleration (I think). Besides, even if I try this method I get the question wrong. The answer from my lecturer is supposedly s=657m.

    I think the above equation must be integrated again to get the displacement but I have tried and I think I'm missing something because I can't manipulate it so that I end up with s in the formula.

    Please help as I have pulled my hair off trying to figure this out to no avail.
     
  2. jcsd
  3. Apr 1, 2010 #2
    What is the value for mass?
     
  4. Apr 1, 2010 #3
    Oops sorry forgot to put that value. Mass is 2000 kg.
     
  5. Apr 3, 2010 #4

    jack action

    User Avatar
    Science Advisor
    Gold Member

    From:

    [tex]ma=F_d[/tex]

    And:

    [tex]a dx=u du[/tex]

    You get:

    [tex]\int dx=\int\frac{m u}{F_d}du[/tex]
     
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