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Two Parachute Problems

  1. Mar 28, 2010 #1
    Hi all,
    So I have these two parachute problems that have been giving me problems any aid you can provide would be much apreciated!

    1. The problem statement, all variables and given/known data
    A)A probe is to land on the surface of mars and I am required to find out the diameter of the parachute.
    Given constance:
    m=40kg
    g=3.75m/s2
    v0=100m/s
    vf= 3m/s
    x0=100m
    Pair=2/3*1.1774
    Cd=1.4
    A=pi*D2/4 (where D is the unknown diameter of the parachute)

    2. Relevant equations

    m[tex]\frac{dV}{dt}[/tex]=mg-[tex]\frac{1}{2}[/tex]Pair*Cd*AV2

    3. The attempt at a solution

    I've seprated the variables and simplified to get:

    g-[tex]\frac{k}{m}[/tex]*V2*dV=dt
    where k=[tex]\frac{1}{2}[/tex]PairCdA
    [tex]\sqrt{}[/tex]
    So i decomposed the function for integration:
    [tex]\int[/tex][tex]\frac{\frac{1}{\sqrt{g}}}{\sqrt{g-\sqrt{\frac{k}{m}}V}}[/tex]+[tex]\frac{\frac{1}{\sqrt{g}}}{\sqrt{g+\sqrt{\frac{k}{m}}V}}[/tex]
    (ignore the second square root on top of the K/m that comes from G, it's only supposed to be on g)

    and so that I've integrated to get the following:

    [tex]\frac{1}{\sqrt{g}*\sqrt{\frac{k}{m}}}(Ln(\sqrt{g}-\sqrt{\frac{k}{m}}V))+Ln(\sqrt{g}-\sqrt{\frac{k}{m}}V))=t+c[/tex]

    At this point I understand that I can raise everything to E and cancel the +-[tex]\sqrt{\frac{k}{m}}V[/tex] but from here I am unsure (also not 100% on the integration)

    Also, I have a similar problem however it's not falling, rather slowing down from a parachute (rocket car slowing down from parachute), where I need to find the distance required to stop the car.

    Where I was given m[tex]\frac{dV}{dt}[/tex]=-[tex]\frac{1}{2}[/tex]Pair*Cd*AV2

    So I integrated as a seperable (don't think this is the right way though) to get
    [tex]\frac{-1}{kV}=t+c[/tex] (a check or direction for this one is all I need)

    Thank you!
     
  2. jcsd
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