Old Man River . . . In Figure 3.2.8(a) suppose that the

Chapter 3, Problem 3.1.76

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Old Man River . . . In Figure 3.2.8(a) suppose that the y-axis and the dashed vertical line x 1 represent, respectively, the straight west and east beaches of a river that is 1 mile wide. The river flows northward with a velocity vr, where mi/h is a constant. A man enters the current at the point (1, 0) on the east shore and swims in a direction and rate relative to the river given by the vector vs, where the speed mi/h is a constant. The man wants to reach the west beach exactly at (0, 0) and so swims in such a manner that keeps his velocity vector vs always directed toward the point (0, 0). Use Figure 3.2.8(b) as an aid in showing that a mathematical model for the path of the swimmer in the river is [Hint: The velocity v of the swimmer along the path or curve shown in Figure 3.2.8 is the resultant v vs vr. Resolve vs and vr into components in the x- and y-directions. If are parametric equationsof the swimmers path, then .]