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Math Help - vector help

  1. #1
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    vector help

    The angle of POW is 45 . In the diagram OP represents
    the velocity of an aircraft cruising at a constant
    velocity of 500 km per hour due north . OW represents
    the constant wind velocity of 50 km per hour . How
    far will the aircraft deviate from its original path after
    it has travelled for 3 hours .








    P W





    O
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  2. #2
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    Quote Originally Posted by mathaddict View Post
    The angle of POW is 45 . In the diagram OP represents
    the velocity of an aircraft cruising at a constant
    velocity of 500 km per hour due north . OW represents
    the constant wind velocity of 50 km per hour . How
    far will the aircraft deviate from its original path after
    it has travelled for 3 hours .
    ...
    Use a coordinate system with the x-axis pointing East and the y-axis pointing North.

    Then the vector which describes the flight of the air plane in one hour is:

    \vec a=(0, 500) and the vector describing the winds movement in one hour is

    \vec w = \dfrac{50}{\sqrt{2}}\cdot (1,1)

    The course over ground of the airplane in t hours is:

    \vec c = t \cdot (\vec a + \vec w )= t \cdot \left(\dfrac{50}{\sqrt{2}}\ ,~ 500+\dfrac{50}{\sqrt{2}}  \right)

    The position of the plane after 3 hours flight will be:

    P\left(\dfrac{150}{\sqrt{2}}\ ,~ 1500+\dfrac{150}{\sqrt{2}}  \right)

    Without any wind the plane would be at P_0\left(0\ ,~ 1500  \right)

    Now calculate the difference between these two places.
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