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24 November, 22:35

A boat travels 30 miles north, 20 miles east and 40 miles northeast. What is the angle of rotation of the boats direction from start to finish

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  1. 25 November, 01:16
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    The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.

    Step-by-step explanation:

    Let x axis be east direction and Y axis be north direction.

    We have first boat travels 30 miles north

    Displacement = 30 j

    20 miles east

    Displacement = 20 i

    40 miles northeast

    Displacement = 40 cos 45 i + 40 sin 45 j = 28.28 i + 28.28 j

    Total displacement = 48.28 i + 58.28 j

    Angle, tanθ = 58.28/48.28

    θ = 50.36⁰

    The angle of rotation of the boats direction from start to finish = 50.36⁰ to east towards north.
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