Question

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.

Answer 1

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

Answer 2

distance = 61.39
time to port = 7.67 hours