Free fall Using the background given in Exercise 62,
Chapter 7, Problem 63(choose chapter or problem)
Free fall Using the background given in Exercise 62, assume the resistance is given by f 1v2 = -Rv, where R 7 0 is a drag coefficient (an assumption often made for a heavy medium such as water or oil). a. Show that the equation can be written in the form v_1t2 = g - bv, where b = R>m. b. For what (positive) value of v is v_1t2 = 0? (This equilibrium solution is called the terminal velocity.) c. Find the solution of this separable equation assuming v102 = 0 and 0 6 v 6 g>b. d. Graph the solution found in part (c) with g = 9.8 m>s2, m = 1 kg, and R = 0.1 kg>s, and verify that the terminal velocity agrees with the value found in part (b).
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