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A fishing boat leaves port at 11 miles per hour at a bearing of 210 degrees for 2 hours, then turns to a bearing of 250 degrees at 8 miles per hour for 4 hours, and finally changes to a bearing of 280 degrees at 7 miles per hour for 2 hours. At this point, the boat heads directly back to port at a speed of 8 miles per hour. Find the time it takes the boat to return to port as well as the boat's bearing as it does.

  • Math -

    break each section into x- and y-components. Starting at (0,0),

    22 @ 210° moves (-11.00,-19.05)
    32 @ 250° moves (-30.07,-10.94)
    14 @ 280° moves (-13.79,2.43)

    Final location: (-54.86,-27.56)

    bearing to port = 63°20'

    distance = 47.43
    time to port = 5.93 hours

  • Math - correction -

    distance = 61.39
    time to port = 7.67 hours

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