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Calc question

  1. May 24, 2007 #1
    1. The problem statement, all variables and given/known data

    A 727 jet needs to attain a speed of 200 mph to take off. If it can accelerate from 0 to 200 mph in 30 seconds, how long must the runway be? (Assume constant accleration). Show all your work and include units in your answer.

    2. Relevant equations

    3. The attempt at a solution

    Since v = dx/dt = 200t

    I took the integral of dx = integral of 200t dt

    and I got x = 100t^2 + C

    So I plugged in 0.5 as t and got x = 25.

    So x = 25 miles? But.. 25 miles sounds wrong for an airplane runway.. where did I go wrong?
     
  2. jcsd
  3. May 24, 2007 #2

    Dick

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    You have time units of both hours, minutes and seconds in your problem. I would suggest before mixing them (and not indicating units) that you convert your numbers to a common time unit.
     
    Last edited: May 24, 2007
  4. May 24, 2007 #3
    Oh, so instead of 0.5, it should've been

    ( (30sec) / (3600sec/hr) ) = t

    so it comes out to 0.0069 miles?

    Thanks again
     
  5. May 24, 2007 #4

    Dick

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    0.0069 miles=about 35 feet. About as bad an estimate as 25 miles. Just convert everything to seconds. You are doing everything correctly mathematically - except the grasp of units is horrible.
     
    Last edited: May 24, 2007
  6. May 24, 2007 #5

    Dick

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    If you've ever taken off in a plane you know the answer is roughly on the order of a mile. Don't rest until you get something in that ballpark.
     
  7. May 24, 2007 #6
    Actually, I don't even think I set it up right after I look at it again, so I'm stuck now.

    v is not 200t (is it?). v is just 200. so dx = 200 dt,
    so, x = 200t

    so (30/3600) hour = t

    plugged it in, got x = 1.6666666666667

    so about 2 miles, that seems right. So did I actually set the problem up wrong?
     
  8. May 25, 2007 #7

    Dick

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    Still wrong. Please start using units, ok? v=at. d=(1/2)*a*t^2. You had it set up just fine. The units are killing you. What it 200 mph in miles/sec?
     
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