Somewhere on the high seas smuggler Stan is attempting, without much luck, to outspeed coast guard Charlie, whose boat can go faster than Stan's. Charlie is one mile east of Stan when a heavy fog descends. It's so heavy that nobody can see or hear anything further than a few feet. Immediately after the fog descends, Stan changes course and attempts to escape at constant speed under a new, fixed course. Meanwhile, Charlie has lost track of Stan. But Charlie happens to know Stan's speed, that it is constant, and that Stan is sticking to some fixed heading, unknown to Charlie.

How does Charlie catch Stan?

Charlie may change course and speed at will. He knows his own speed and course at all times. There is no wind, Charlie does not have radio or radar, there is enough space for maneuvering, etc.

I don't know how relevant this is, but this situation came up in the hunt for the German battleship Bismark in World War II.

Two British cruisers were trailing the Bismark. Her commander gave the order that she begin zigzagging, and then in the middle of the night she was to stop zigzagging and make off at constant speed in whatever direction she was headed at that time. The cruisers were forced to zigzag when they saw Bismark doing so, as they dared not get too close to the latter's 16 inch guns.

In the middle of the night, the Bismark stopped zigzagging and made off at a constant direction and speed.

The cruisers lost the Bismark and she succeeded in evading them.  

Posted by Penny on 2005-11-01 21:43:57