Coughing velocity. A person coughs when a foreign object is in the windpipe. The

Chapter 2, Problem 107

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Coughing velocity. A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the size of the object. Suppose a person has a windpipe with a 20-mm radius. If a foreign object has a radius r, in millimeters, then the velocity V, in millimeters per second, needed to remove the object by a cough is given by where k is some positive constant. For what size object is the maximum velocity required to remove the object?

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