A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 5.3, Problem 18E

Pursuit curve In another naval exercise a destroyer S₁ pursues a submerged submarine S₂. Suppose that S₁ at (9, 0) on the x-axis detects S₂ at (0, 0) and that S₂ simultaneously detects S₁. The captain of the destroyer S₁ assumes that the submarine will take immediate evasive action and conjectures that its likely new course is the straight line indicated in Figure 5.3.10. When S₁ is at (3, 0), it changes from its straight-line course toward the origin to a pursuit curve C. Assume that the speed of the destroyer is, at all times, a constant 30 mi/h and that the submarine’s speed is a constant 15 mi/h.

(a) Explain why the captain waits until S₁ reaches (3, 0) before ordering a course change to C.
(b) Using polar coordinates, find an equation r = f (θ) for the curve C.
(c) Let T denote the time, measured from the initial detection, at which the destroyer intercepts the submarine. Find an upper bound for T.

Chapter 5.3, Problem 18E, Pursuit curve In another naval exercise a destroyer S1 pursues a submerged submarine S2. Suppose

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Chapter 5.3, Problem 17E

Chapter 5.3, Problem 19E

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Chapter 5 Solutions

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Ch. 5.1 - 5.1.1 Spring/Mass systems: Free Undamped Motion A...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A force...Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Spring/Mass Systems: Free Undamped Motion A mass...Ch. 5.1 - 5.1.1Spring/Mass Systems: Free Undamped Motion A...

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