Pursuit Curve In a naval exercise, a ship S 1 is pursued by a submarine S2, as shown in

Chapter 3, Problem 19

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Pursuit Curve In a naval exercise, a ship S 1 is pursued by a submarine S2, as shown in FIGURE 3.11.8. Ship S1 departs point (0, 0) at t = 0 and proceeds along a straight-line course (the y-axis) at a constant speed v1 The submarine S2 keeps ship S1 in visual contact, indicated by the straight dashed line L in the figure, while traveling at a constant speed v2 along a curve C. Assume that S2 starts at the point (a, 0), a > 0, at t = 0 and that Lis tangent to C. Determine a mathematical model that describes the curve C. Find an explicit nience, define solution r = of vifv1 the differential Determine equation. whether the For paths conveof S 1 and S2 will ever intersect by considering the cases r > 1, r < 1, and r = 1. [Hint: dt = dt ds, wheres is arc length measured along C.] dx ds dx ----!----------% RGURE3.1U Pursuitauvein 19