Math CentralQuandaries & Queries


Question from Laura, a student:

A ship leaves its home port and sails on a bearing of N28.17°E. Another ship leaves the same port at the same time and sails on a bearing of S61.83E. If the first ship sails at 24 mph and the second at 28 mph find the distance between the two ships after 4 hours.


Despite the bogus precision of the bearings (no helmsperson can hold a course to a hundredth of a degree: one degree is doing well. ) I'm assuming that the curvature of the earth may be ignored.

(And what sort of landlubber measures vessel speed in mph rather than knots? Aaaarh, lass, knots were good enough for Blackbeard and Anne Bonny, and they're good enough for the Dread Pirate Roberts.)

Now find the angular difference between the two courses. You may be able to do this in your head, if you understand the notation. [The correct answer is tidy.]

Hints if needed:
N28.17E means 28.17 degrees clockwise (towards East) of North: like the slanting line here: |/
S61.83E means 61.83 degrees counterclockwise (towards East) of South, like the slanting line here but less vertical: |\
North and South are 180 degrees apart.

Now find the distances (velocity * time) and draw a diagram. Use trig to finish.

Good Hunting!

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