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Plane towing two gliders

  1. Sep 17, 2005 #1
    A transport plane has two gliders tied behind it. The max force allowable on the tow rope is 12000N. The mass of each glider is 700kg. A velocity of 40 m/s is required to take off. What is the minimum runway space required.


    The solution I have arrived at doesn't seem correct, hopefully someone can tell me where I have strayed off the path.

    F = ma

    12000 = (700+700)a
    a = 12000/1400
    a = 8.57 m/s^2



    V = V(init) +at

    40 = 0 +8.57t
    t = 40/8.57
    t = 4.67s



    S = 1/2(a)t^2+V(init)t + S(init)

    1/2(8.57)(4.67^2) + 0 + 0 = 20 meters


    I don't think the plane could reach 40 m/s in 4.67 seconds and it would have to be a really small transport plane to take off in 20 meters. Hopefully someone can point out where I went wrong.

    Thanks for the help.
     
  2. jcsd
  3. Sep 18, 2005 #2

    Fermat

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    You forgot to square the 4.67 value. It should be about 93m

    4.67s does seem a bit short, but 93 m seems ok!
     
  4. Sep 18, 2005 #3
    Huh, After checking my work a few times I still missed that one. Thanks!
     
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