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16 February, 10:34

A boat travels at 15 m/s in a direction 45° east of north for an hour. The boat then turns and travels at 18 m/s in a direction 5° north of east for an hour.

What is the magnitude of the boat's resultant velocity? Round your answer to the nearest whole number.

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  1. 16 February, 11:13
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    16 m/s

    Explanation:

    First, find the displacement in the east direction.

    x = (15 m/s sin 45°) (3600 s) + (18 m/s cos 5°) (3600 s)

    x = 102,737 m

    Next, find the displacement in the north direction.

    y = (15 m/s cos 45°) (3600 s) + (18 m/s sin 5°) (3600 s)

    y = 43,831 m

    Find the magnitude of the displacement.

    d = √ (x² + y²)

    d = √ ((102,737 m) ² + (43,831 m) ²)

    d = 111,697 m

    Finally, find the resultant velocity.

    v = d / t

    v = (111,697 m) / (7200 s)

    v = 15.5 m/s

    Rounded to the nearest whole number, the resultant velocity is 16 m/s.
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