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10 October, 19:06

A delivery man starts at the post office, drives 40 km north, then 20 km west, then 60 km northeast, and finally 50 km north to stop for lunch. use a graphical method to find his net displacement vector.

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  1. 10 October, 19:44
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    assuming north-south along the Y-axis and east-west along the X-axis

    X = total X-displacement

    from the graph, total displacement along X-direction is given as

    X = 0 - 20 + 60 Cos45 + 0

    X = 42.42 - 20

    X = 22.42 m

    Y = total Y - displacement

    from the graph, total displacement along Y-direction is given as

    Y = 40 + 0 + 60 Sin45 + 50

    Y = 90 + 42.42

    Y = 132.42 m

    magnitude of the net displacement vector using Pythagorean theorem is given as

    magnitude : Sqrt (X² + Y²) = Sqrt (22.42² + 132.42²) = 134.31 m

    Direction : tan⁻¹ (Y/X) = tan⁻¹ (132.42/22.42) = 80.4 deg north of east
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