Suppose a wolf is chasing a rabbit. The path ofthe wolftoward the rabbit is called a

Chapter 5, Problem 5

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Suppose a wolf is chasing a rabbit. The path ofthe wolftoward the rabbit is called a curve of pursuit. Assume the wolf runs at the constant speed a and the rabbit at the constant speed /I. Let the wolf begin at time / = 0 at the origin and the rabbit at the point (0, 1). Assume the rabbit runs up the line x = 1. Let (x(t), y(t)) denote the position ofthe wolf attime t. The differential equation describing the curve of pursuit is ax 2 Suppose the wolf runs at the speed 35 miles per hour and the rabbit runs at the speed 25 miles per hour. Find the location (x(/), y{t)) where the wolf catches the rabbit using the Extrapolation method with TOL = 1()-|H , hmin = KT12 , and hmax =0.1.