A small boat is headed for a harbor 31 km directly northwest of its current posi

Question

A small boat is headed for a harbor 31 km directly northwest of its current position when it is suddenly engulfed in heavy fog. The captain maintains a compass bearing of northwest and a speed of 10.1 km/h relative to the water. The fog lifts 3.0 h later and the captain notes that he is now exactly 3.9 km south of the harbor.
(a) What was the average speed of the current during those 3.0 h?
(b) In what direction should the boat have been heading to reach its destination along a straight course?
the answer is an angle west of north
(c) What would its travel time have been if it had followed a straight course?

Explanation / Answer

a) The distance, x = 3.9 km    The time, t = 3 hr So the average speed of the current during those 3.0 h is
     Vc = 3.9/3 = 1.3 k/h

b) direction should the boat have been heading to reach its destination along a straight course is 40.55°
c) Travel time have been if it had followed a straight course is given by t = 3.0*cos40.55°/cos45° = 3.22 hr

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