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Math Help - Vectors

  1. #1
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    Vectors

    A plane flies on a bearing of 120 degrees at a constant speed of 550 km/h. If the velocity of the wind is 50 km/h on a bearing 220 degrees, what is the velocity of the plane with respect to the ground?

    Textbook Answer: 543.5 km/h at a bearing of 125.2 degrees

    My answer: 543.6 km/h at a bearing of 175 degrees

    My work:

    Let vector w represent 50 km/h
    Let vector v represent 550 km/h
    Let vector r represent the resultant

    I'm using component vectors. . .

    w = (50cos220 , 50sin220)
    w = (-38.3 , -32.1)

    v = (550cos120 , 550sin120)
    v = (-275 , 476.3)

    r = (-38.3 , -32.1) + (-275 , 476.3)
    r = (-313.3 , 444.2)

    To find the resultant:
    | r | = (-313.3)^2 + (444.2)^2
    | r | = (sqrt)295 470.53
    | r | = 543.6 km/h

    To find the angle:
    tanx = 444.2/-313.3
    x = 55 degrees

    120 + 55 = 175 (To find the bearing)

    ----------------What did I do wrong? How can I get the 125 degree instead of 175 degrees?
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  2. #2
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    Quote Originally Posted by Macleef View Post
    ...
    To find the angle:
    tanx = 444.2/-313.3
    x = 55 degrees

    120 + 55 = 175 (To find the bearing)

    ----------------What did I do wrong? How can I get the 125 degree instead of 175 degrees?
    With \tan(x)=\frac{44.2}{-313.3} you calculate the bearing directly:

    \tan(x)=\frac{44.2}{-313.3}~\implies~ x=-54.8^\circ

    Since bearings are given as positive numbers add 180 and you'll get the result given by your book.
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