For a fish swimming at a speed v relative to the water, the energy expenditure p

Q: For a fish swimming at a speed v relative to the water, the energy expenditure p

v = 3u/2. To determine the value of v that minimizes E, solve the equation E'(v) = 0. E(v) = (av^3) * (L/(v - u)). Use that if f(x) = g(x)*h(x), then f'(x) = g'(x)*h(x) + g(x)*h'(x).

ID: 2828020 • Letter: F

Question

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. 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 < 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 the formula below, where a is the proportionality constant.
E(v) = av^3 L/(v - u)
Determine the value of v that minimizes E. (Note: This result has been verified experimentally.)

Explanation / Answer

v = 3u/2.

To determine the value of v that minimizes E, solve the equation E'(v) = 0.
E(v) = (av^3) * (L/(v - u)).
Use that if f(x) = g(x)*h(x), then f'(x) = g'(x)*h(x) + g(x)*h'(x).

Navigate

For a first-order reaction, what fraction of the starting material will remain a

For a fish swimming at a speed v relative to the water, the energy expenditure p

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.

For a fish swimming at a speed v relative to the water, the energy expenditure p

Question

Explanation / Answer

Related Questions

Navigate