A boat travels with velocity vector (25, 25 StartRoot 3 EndRoot). What is the directional bearing of the boat? N 30° E E 30° S E 30° N N 30°

Question

A boat travels with velocity vector (25, 25 StartRoot 3 EndRoot). What is the directional bearing of the boat? N 30° E E 30° S E 30° N N 30° W

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Amity 3 weeks 2021-08-26T18:11:39+00:00 2 Answers 0 views 0

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    0
    2021-08-26T18:12:44+00:00

    Answer:

    a

    Step-by-step explanation:

    0
    2021-08-26T18:12:55+00:00

    Answer:

    The directional bearing of the boat is N 30º E

    Step-by-step explanation:

    Let \vec v = (25, 25\sqrt{3}), where \vec v is the vector velocity. Given that such vector is represented in rectangular, a positive value in the first component is the value of the vector in the east direction, whereas a positive value in the second component is in the north direction. The directional bearing of the boat (\theta), measured in sexagesimal degrees, is determined by trigonometrical means:

    \theta = \tan^{-1}\frac{v_{y}}{v_{x}} (1)

    If we know that v_{x} = 25 and v_{y} = 25\sqrt{3}, then the directional bearing of the boat is:

    \theta = \tan^{-1} \sqrt{3}

    \theta = 60^{\circ}

    In consequence, we conclude that the direction bearing of the boat is 30 degrees to the East from the North (N 30º E).

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