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Math Help - Did I do this vector question right?

  1. #1
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    Did I do this vector question right?

    A plane is heading S 70degrees W with a groundspeed of 625km/h. If the pilot is steering west at an airspeed of 665km/h, what must be the windspeed and wind direction?

    This is the diagram I drew, forgive me if the scaling is off:



    The magnitude of the wind I found was:

    w^2 = a^2 + g^2 -2(a)(g)(cos110degrees)

    = about 1057 km/h

    Is this wrong? I want to know if I have the right answer for the magnitude before attempting to find the direction of the wind.
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  2. #2
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    w^2 = a^2 + g^2 - 2ag \cos(20)<br />
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  3. #3
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    Hello, kmjt!

    Your diagram is incorrect . . .


    A plane is heading S 70 W with a groundspeed of 625 km/h.
    If the pilot is steering west at an airspeed of 665 km/h,
    . . what must be the windspeed and wind direction?
    Code:
                     665
        A o - - - - - - - - - - - o O
           \               20 *
            \               *
             \           *
              \       *  625
               \   *
                o
                B

    The plane is flying from O to A at 665 km/hr.
    . . \angle AOB = 20^o

    The wind is blowing from A to B.

    The plane's resultant flight is: . OB = 625 km/hr.


    Law of Cosines: . AB^2 \:=\:665^2 + 625^2 - 2(665)(625)\cos20^o \;=\;51,\!730.50897

    . . Hence: . AB \;\approx\;227.4


    Then: . \cos A \;=\;\frac{665^2 + 227.4^2 - 625^2}{2(665)(227.4)} \;=\;0.341588668

    . . Hnce: . \angle A \;\approx\;70^o


    Therefore, the windspeed is 227.4 km/hr and its direction is: .S 20 E.



    Interesting!
    Triangle ABO is virtually a right triangle . . .
    .
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  4. #4
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    Doh thats what I got the first time I just thought it was wrong because usually we have to calculate something to find what angle the wind is blowing at.. Thanks
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