Pursuit Curve In a naval exercise a ship S1 is pursued by a submarine S2 as shown in Figure 5.3.8. Ship S1 departs point (0, 0) at t 0 and proceeds along a straightline 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 ship S2 starts at the point (a, 0), a 0, at t 0 and that L is tangent to C. (a) Determine a mathematical model that describes the curve C. (b) Find an explicit solution of the differential equation. For convenience define r v1v2. (c) Determine whether the paths of S1 and S2 will ever intersect by considering the cases r 1, r 1, and r 1. [Hint: , where s is arc length measured along C.] dt

MATH 415 { Lecture 1 Solving linear systems Wednesday 18 Jan 2016 Textbook reading: Chapter 1.3, Chapter 2.2 (only pages 78 and 79) Suggested practice exercises: Chapter 1.3: 1, 3, 5, 6, 11, 17, 23, 24. Chap- ter 2.2: 2, 8. Khan Academy Video: Matrices: Reduced Row Echelon Form 1 1 Systems of Linear...