In another naval exercise a destroyer S 1 pursues a submerged submarine S 2 Suppose that S 1 at (9, 0) on the x axis detects S 2 at (0, 0) and that S 2 simultaneously detects S1 The captain of the destroyer S 1 assumes that the submarine will take immediate evasive action and conjectures that its l...

Given that a Let r denote the polar ordinates of the destroyer s 1 when s 1 tr ...

In another naval exercise a destroyer S 1 pursues a submerged submarine S 2 . Suppose that

Question:

In another naval exercise a destroyer S₁ pursues a submerged submarine S₂. Suppose that S₁at (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 5.3.9. 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 (u) 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.

Figure 5.3.9.

S2 (3, 0) (9, 0)*