Graph of swimming fish energy

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Reference no: EM13123658

"For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. 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 u(u less than v), then the time required to swim a distance L is L/(v-u) and the total energy E required to swim the distance is given by

E(v)=av^3(L/[v-u])

where a is the proportionality constant.

(a) Determine the value of v that minimizes E.

(b) Sketch the graph of E.

Author's Note: This result has been verified experimentally; migrating fish swim against a current at a speed of 50% greater than the current speed."

Reference no: EM13123658

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