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Math Help - Vector question (relative speed)

  1. #1
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    Vector question (relative speed)

    A plane goes from city A to city B. In a Cartesian plane, city A is at the origin and city B has coordinates (100,150). If there is no wind, the flight lasts one hour. Unfortunately, there is a wind. If the pilot does not adjust his flight path, he will be at point (120,160) after an hour. What is the speed of the wind?

    I am having trouble doing this question, and my teacher has warned there will be a question similar to this on our test. I would like to know the steps I need to take in order to solve this question.
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  2. #2
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    Hello, Solid8Snake!

    A plane goes from city A to city B. In a Cartesian plane.
    City A is at the origin and city B has coordinates (100,150).
    If there is no wind, the flight lasts one hour. Unfortunately, there is a wind.
    If the pilot does not adjust his flight path, he will be at point (120,160) after an hour.
    What is the speed of the wind?
    Code:
          |                             C
          |                             o(120,160)
          |                          * *
          |                       *   *
          |                    *     *
          |                 *       *
          |              *         *
          |           *           o(100,150)
          |        *        *     B
          |     *     *
          |  *  *
        A * - - - - - - - - - - - - - - - - - - -
          |

    The plane's original vector was: . \overrightarrow{AB} \:=\:\langle100,150\rangle

    Due to the wind, \overrightarrow{BC} \:=\:\langle x,y\rangle, it flies to C(120,160).


    Since \overrightarrow{AB} + \overrightarrow{BC} \:=\:\overrightarrow{AC}, we have: . \langle 100,150\rangle + \langle x,y\rangle \:=\:\langle120,160\rangle

    . . Hence: . \begin{array}{ccccccc}100 + x \:=\:120 & \Longrightarrow & x \:=\:20 \\ 150 + y \:=\:160 & \Longrightarrow & y \:=\:10 \end{array}


    The wind's vector is: . \overrightarrow{BC} \:=\:\langle 20,10\rangle

    Its speed (magnitude) is: . |\overrightarrow{BC}| \;=\;\sqrt{20^2+10^2} \;=\;\sqrt{500} \;=\;10\sqrt{5}

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  3. #3
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    thx a million
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