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Trawler Problem


A fast boat is overtaking a slower one when fog suddenly sets in. At this point, the boat being pursued changes course, but not speed, and proceeds straight in a new direction which is not known to the fast boat. How should the pursuing vessel proceed in order to be sure of catching the other boat?

The amazing answer is that the pursuing boat should continue to the point where the slow boat would be if it had set its course directly for the pursuing boat when the fog set in. If the boat is not there, it should proceed in a spiral whose origin is the point where the slow boat was when the fog set in. The spiral must be constructed in such a way that, while circling the origin, the fast boat's distance from it increases at the same rate as the boat being pursued. The two courses must therefore intersect before the fast boat has completed one 360 degrees circuit. In order to make the problem reasonably practical, the fast boat should be capable of maintaining a speed four or five times as fast as the slow boat. Also, if the fast boat's speed remains constant, the spiral must be logarithmic.

The Season 3 episode "Spree, Part 2" (2007) of the television crime drama NUMB3RS featured an urban permutation of the trawler problem.


See also

Apollonius Pursuit Problem, Logarithmic Spiral, Pursuit Curve

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References

Agnew, R. P. Differential Equations. New York: McGraw-Hill, p. 303, 1942.Ford, L. R. Differential Equations. New York: McGraw-Hill, p. 32, 1955.Ogilvy, C. S. Excursions in Mathematics. New York: Dover, pp. 84 and 148, 1994.

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Trawler Problem

Cite this as:

Weisstein, Eric W. "Trawler Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TrawlerProblem.html

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