For small, slowly falling objects, the assumption made in

Chapter 1, Problem 25

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For small, slowly falling objects, the assumption made in the text that the drag force is proportional to the velocity is a good one. For larger, more rapidly falling objects, it is more accurate to assume that the drag force is proportional to the square of the velocity.2 (a) Write a differential equation for the velocity of a falling object of mass m if the magnitude of the drag force is proportional to the square of the velocity and its direction is opposite to that of the velocity (b) Determine the limiting velocity after a long time. (c) If m = 10 kg, find the drag coefficient so that the limiting velocity is 49 m/s. (d) Using the data in part (c), draw a direction field and compare it with Figure 1.1.3.