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.

Debunking the spiral strategem:

The faster Coast Guard patrol boats have a maximum speed of 55 to 60 knots.  Let's assume that Charlie is in one of these fast boats while Stan's boat travels at the more modest speed of 45 knots.  If Charlie plans to follow a spiral path that begins at Stan's last known position, it will take him approximately 52 seconds to get there, at top speed.  By that time, Stan is already .39 knots away.  In order to follow the optimum spiral path, Charlie would have to travel ��2 * 45 knots = 63 knots from the start, just to keep from losing ground.  That's already above his boat's ability.  Unless Charlie is just plain lucky with a guess about the right direction, Stan will be long gone before the fog lifts and shows that Charlie was just spinning in circles. 

Not a very rigorous "proof", I know.  Of course, if Charlie travels fast enough in very tight circles, he might create a whirpool that sucks Stan right back to the starting point.

Edited on November 5, 2005, 11:57 am

Posted by Mindy Rodriguez on 2005-11-04 20:20:28