Old Man River Keeps Moving . . . Suppose the man in again enters the current at (1, 0) but this time decides to swim so that his velocity vector vs is always directed toward the west beach. Assume that the speed mi/h is a constant. Show that a mathematical model for the path of the swimmer in the river is now (reference problem 28)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 equations of the swimmer’s path, then .]

Chapter 1 Introduction Physics o The study of nature The Domains of Physics o Microscopic Domain The domain of atoms, molecules, electrons, protons, pion and mesons, etc. Extreme small in mass Uncertainty of physical properties Unpredictable behavior o Macroscopic...