calc 3

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The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 200 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.)

  • calc 3 -

    Trouble-free way to get resultant:
    resolve into x- and y-components and add.
    Wind is FROM N45W, which means that its direction is S45E.
    Take East = x, and North = y,
    the wind vector is then
    <40sin(45),40cos(45)>

    The velocity vector of the plane is
    <200sin(60),200cos(60)>

    The combined vector (resultant) is therefore
    <40sin(45)+200sin(60), 40cos(45)+200cos(60)>
    Find the magnitude and direction of the resultant in the usual way.

  • calc 3 -

    22

  • calc 3 -

    41.6

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