Finding length of airport runway

  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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    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. 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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    Your conversion of km/hr to m/s is wrong.
    The plane is slowing down. So the acceleration must be negative.
     
  6. 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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    300km/hr = 300*1000/3600 = ? m/s
     
  8. 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. rl.bhat

    rl.bhat 4,433
    Homework Helper

    Now the answer is correct.
     
  10. thanks so much rl. you are a legend
     
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