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A car is driven east for a distance of 44 km, then north for 25 km, and then in a direction 27° east of north for 28 km. Determine (a) the magnitude (in km) of the car's total displacement from its starting point and (b) the angle (from east) of the car's total displacement measured from its starting direction.

  • physic - ,

    Add the three displacement vectors.

    44i + 25j + 28sin27i + 28cos27j
    = (44+28sin27)i + (25 +cos27)j

    i and j are unit vectors east and north

    Use the Pythagoreaqn theorem for the magnitude and the ratio of components for the tangent of the direction.

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