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Finding cross-sectional area from terminal velocity.

  1. Dec 24, 2013 #1
    1. The problem statement, all variables and given/known data

    The aerodynamic drag on an object moving through air is proportional to Av^2, where A=cross-section, and v=velocity. The terminal velocity of a person without a parachute falling through the air is about 56m/s. Estimate the area of the cross-section of a person seen from the front.


    2. Relevant equations



    3. The attempt at a solution

    I'm quite flummoxed by this one. We're told only that drag is propotional to Av^2. Anyway, I began by saying that for terminal velocity to be reached, the drag-force must equal the gravity-force, i.e. D = mg. But, I'm unsure how to proceed from there. I'm not told the mass of the person, nor the drag coefficient, so I really don't know how to find A. I'm sure the use of the word "estimate" here is significant. Maybe I'm expected to find the average human mass, and use that, but then that leaves me still without a complete equation, as I'm told the two are proportional.

    The answer given in the textbook is 0.6m^2.

    Help?
     
  2. jcsd
  3. Dec 24, 2013 #2

    haruspex

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    You certainly have not been given enough information. As it happens, the drag coefficient for an arbitrary convex body tends to be about 1, but you still need to bring in the mass of the person and the density of the air.
    I suppose you could relate the mass of the person to the cross-sectional area, assuming the person's density to be that of water, but that isn't quite straightforward.
    This link might help: http://en.wikipedia.org/wiki/Drag_coefficient
     
  4. Dec 24, 2013 #3
    Cheers, haruspex. I'll have to speak with my physics tutor and see if there's something I'm overlooking. Damn the holidays.
     
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