For a fish swimming at a speed relative to the water, the energy expenditure per unit
Chapter 4, Problem 38(choose chapter or problem)
For a fish swimming at a speed relative to the water, the energy expenditure per unit time is proportional to . It is believed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current , then the time required to swim a distance is and the total energy required to swim the distance is given by where is the proportionality constant. (a) Determine the value of that minimizes . (b) Sketch the graph of . Note: This result has been verified experimentally; migrating fish swim against a current at a speed greater than the current speed.
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