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15 March, 04:48

A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E. The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E. At that time, how far is the boat from the harbor entrance, and what is the bearing of the boat from the harbor entrance?

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  1. 15 March, 07:20
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    Step-by-step explanation:

    A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.

    Displacement in vector form

    = 28 cos43 i + 28sin43j

    = 20.47 i + 19.1 j

    The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E

    Displacement

    = 15 cos47 i - 15 sin47 j

    = 10.22 i - 10.97 j

    Total displacement

    = 20.47 i + 19.1 j + 10.22 i - 10.97 j

    = 30.69 i - 8.13 j

    Magnitude of displacement

    = 31.75 miles

    Angle with east direction

    TanФ = - 8.13 / 30.69

    Ф = 15 degree south of east.
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