Air Resistance In (14) of Section 1.3 we saw that a differential equation describing the

Chapter 2, Problem 35

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Air Resistance In (14) of Section 1.3 we saw that a differential equation describing the velocity v of a falling mass subject to air resistance proportional to the instantaneous velocity is dv m- =mg - kv dt ' where k > 0 is a constant of proportionality called the drag coefficient. The positive direction is downward. (a) Solve the equation subject to the initial condition v(O) = v0 (b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. We saw how to determine the terminal velocity without solving the DE in in Exercises 2.1. (c) If the distances, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v, find an explicit expression for s(t) if s(O) = 0.