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.
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.
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