For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v. 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 he time required to swim a distance L is L/(v-u) and the total energy E required to swim the distance is given by L E(v) = av³. v – u where a is the proportionality constant. Determine the value of v that minimizes E. (Your answer may depend on L, u and a).
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v. 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 he time required to swim a distance L is L/(v-u) and the total energy E required to swim the distance is given by L E(v) = av³. v – u where a is the proportionality constant. Determine the value of v that minimizes E. (Your answer may depend on L, u and a).
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
Related questions
Question
Transcribed Image Text:For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v. 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
L
E(v) = av³-
у — и
where a is the proportionality constant.
Determine the value of v that minimizes E. (Your answer may depend on L, u and a).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning