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Math Help - Applications of Vector Addition

  1. #1
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    Applications of Vector Addition

    Hi, just wondering if anybody could help me with the following vector word problem.

    An airplane is flying at 550 km/h on a heading of 080 degrees. The wind is blowing at 60 km/h from a bearing of 120 degrees.
    1) Draw a vector diagram
    2) Find the ground velocity of the airplane

    I'm not sure if I should be using true bearings or quadrant bearings for the diagram, and every time I work out the velocity/bearing I get a different answer than the one provided at the back of my textbook.

    Would appreciate any help, thanks
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  2. #2
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    Lexington, MA (USA)
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    Hello, sam314159265!

    An airplane is flying at 550 km/hr on a bearing of 80.
    The wind is blowing at 60 km/hr from a bearing of 120.

    1) Draw a vector diagram

    2) Find the ground velocity of the airplane
    Code:
                  C         Q
          P       o         *
          *      *  *  60   :
          :     *     *     :
          :    *        *60:
          :   *           * :
          :  *        40   o B
          : *         *  80:
          :*    *  550      :
        A o                 *
                            R

    The plane flies from A to B\!:\;AB \,=\, 550,\;\angle PAB \,=\, 80^o \,=\,\angle ABR

    The wind is blowing from the southeast: . BC \,=\,60,\;\angle QBC \,=\,60^o

    Hence: . \angle ABC \,=\,40^o


    Law of Cosines: . AC^2 \;=\;550^2 + 60^2 - 2(550)(60)\cos40^o \;=\;255,\!541,0668

    . . Hence: . AC \;=\;505.6510699 \;\approx\;505.5 km/hr.


    Law of Cosines: . \cos(\angle CAB) \;=\;\frac{550^2 + 505.5^2 - 60^2}{2(550)(505.5)} \;=\;0.997087043

    . . Hence: . \angle CAB \;=\;4.374216288^o \;\approx\;4.4^o

    Then: . \angle PAC \;=\;\angle PAB - \angle CAB \;=\;80^o - 4.4^o \;=\;75.6^o


    Therefore, the plane is flying at 505.5 km/hr at a bearing of 75.6.

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  3. #3
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    Thank you for your help.
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