Question

A ship leaves port and travels due west for 30 knots, then changes course to S 30° W and travels 50 more knots. Find the bearing from the port of departure

Answer 1

232°

Explanation:

There are a couple of ways to find the desired direction. Perhaps the most straightforward is to add up the coordinates of the travel vectors.

30∠270° +50∠210° = 30(cos(270°), sin(270°)) +50(cos(210°), sin(210°))

= (0, -30) +(-43.301, -25) = (-43.301, -55)

Then the angle from port is ...

arctan(-55/-43.301) ≈ 231.79° . . . . . . . 3rd quadrant angle

The bearing of the ship from port is about 232°.

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Comment on the problem statement

The term "knot" is conventionally used to indicate a measure of speed (nautical mile per hour), not distance. It is derived from the use of a knotted rope to estimate speed. Knots on the rope were typically 47 ft 3 inches apart. As a measure of distance 30 knots is about 1417.5 feet.