Concept explainers
Terminal Velocity In Section 1.3 we saw that the autonomous differential equation
where k is a positive constant and g is the acceleration due to gravity, is a model for the velocity v of a body of mass m that is falling under the influence of gravity. Because the term −kv represents air resistance, the velocity of a body falling from a great height does not increase without bound as time t increases. Use a phase portrait of the differential equation to find the limiting, or terminal, velocity of the body. Explain your reasoning.
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First Course in Differential Equations (Instructor's)
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