# Chases and Escapes: The Mathematics of Pursuit and Evasion

By Paul J. Nahin | Go to book overview

Appendix F
Solution to the Challenge
Problem of Section 2.5

From equation (2.5.8) we have the length r of the position vector to the coast-guard boat, on its outward spiral path, as

where d is the initial distance between the rum runner and the coastguard boat, and k1 and k2 are the speeds of the rum runner and the coast-guard boat, respectively. In polar coordinates the differential arc length ds satisfies (ds)2 = (dr)2 + (rdθ)2, and so the length of the spiral path travelled by the coast guard boat is

Since

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