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Finding length of airport runway

  1. Sep 21, 2009 #1
    the landing speed of a jumbo jet is 300Kn/hr. After landing, the jet comes to the safe taxiing speed of 30Km/hr in 12 seconds. The airport authorities would like to keep a saftey margin of 250 metres of runway. How long should the runway be for the safe landing of jumbo jets?

    Now, I remember doing this in class. I just can't find my notes.

    I was thinking that it might have something to do with:

    Final velocity(v)= initial velocity(u)+acceleration(a) x time(t)

    maybe re-arranging it then being able to find the distance travelled.
    so:
    a=(u-v)/t

    all help appreciated
     
  2. jcsd
  3. Sep 21, 2009 #2

    rl.bhat

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    Your formula for a is correct. Convert km/h to m/s and find the acceleration.
    There is a kinematic equation which contains vi,a,t and x. Using that equation find x.To it add safety margin to find the length of the run way.
     
  4. Sep 21, 2009 #3
    ok. from what you've said this is what i've tried
    u=300km/hr=1080m/s
    v=30km/hr=108m/s
    t=12s
    safety margin=250m

    to get a
    a=(u-v)/t
    =(1080-108)/12
    =81m/s

    so: distance covered=u.t + 1/2.a.t^2
    =(1080 x 12) + (1/2 x 81 x 144)
    =12960 + 5832
    =18792m
    then add the safety margin
    =18792 + 250
    = 19042m
    = 19.042km

    am I any closer to the answer do you think?
     
  5. Sep 21, 2009 #4

    rl.bhat

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    Your conversion of km/hr to m/s is wrong.
    The plane is slowing down. So the acceleration must be negative.
     
  6. Sep 21, 2009 #5
    ok so it would be
    a=(v-u)/t
    =(108-1080)/12
    =-81m/s

    so: distance covered=u.t + 1/2.a.t^2
    =(1080 x 12) + (1/2 x -81 x 144)
    =12960 + -360
    =12600m
    then add the safety margin
    =12600 + 250
    = 12850m
    = 12.85km
    maybe?
     
  7. Sep 21, 2009 #6

    rl.bhat

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    300km/hr = 300*1000/3600 = ? m/s
     
  8. Sep 21, 2009 #7
    had that the first time and thought i was wrong.
    that being the case
    so: distance covered=u.t + 1/2.a.t^2
    =(83.33 x 12) + (1/2 x -6.25 x 144)
    =999 + -450
    =549m
    then add the safety margin
    =549 + 250
    = 799m
    = 0.799km
    you must hate me by now =]
     
  9. Sep 21, 2009 #8

    rl.bhat

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    Now the answer is correct.
     
  10. Sep 23, 2009 #9
    thanks so much rl. you are a legend
     
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