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Wind velocity and aircraft (answer check)

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data

    You’re a pilot beginning a 1500-km flight. Your plane’s speed is 1000 km/h, and air traffic control says you’ll have to head 15° west of south to maintain a southward course. If the flight takes 100 min, what’s the wind velocity?


    3. The attempt at a solution

    veffective south = vactual + vwind

    veffective south = 1500kmh^-1 / 1.667hr = ( 0, -900kmh^-1 )

    vactual = (1000kmh^-1 cos 255, 1000kmh^-1 sin 255) = (-258.82kmh^-1 , -965.93kmh^-1)

    vwind = veffective south - vactual

    therefore

    (0, -900kmh^-1 ) - (-258,82kmh^-1, -965.93kmh^-1)
    = (258.82kmh^-1 , 65.93kmh^-1)
    = |vwind| = SQRT [ (258.82kmh^-1)^2 + (65.93kmh^-1) ^2]
     
    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 15, 2014 #2

    SteamKing

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    I think you should punch the final numbers in your calculator, take the square root, and come up with one number for the answer.
     
  4. Jan 15, 2014 #3
    The answer is 267kmh^-1
     
  5. Jan 15, 2014 #4

    haruspex

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    I confirm that answer.
     
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