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# Ornithologists have determined that some species of birds tend to avoid ights over large

ISBN: 9780495559726 334

## Solution for problem 59 Chapter 4.6

Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition

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Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) | 4th Edition

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Problem 59

Ornithologists have determined that some species of birds tend to avoid ights over large bodies of water during daylight hours. It is believed that more energy is required to y over water than over land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 5 km from the nearest point on a straight shoreline, ies to a point on the shoreline, and then ies along the shoreline to its nesting area . Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points and are 13 km apart. (a) In general, if it takes 1.4 times as much energy to y over water as it does over land, to what point should the bird y in order to minimize the total energy expended in returning to its nesting area? (b) Let and L denote the energy (in joules) per kilometer own over water and land, respectively. What would a large value of the ratio WL mean in terms of the birds ight? What would a small value mean? Determine the ratio corresponding to the minimum expenditure of energy. (c) What should the value of be in order for the bird to y directly to its nesting area ? What should the value of be for the bird to y to and then along the shore to ? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 4 km from B, how many times more energy does it take a bird to y over water than over land?

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##### ISBN: 9780495559726

Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series) was written by and is associated to the ISBN: 9780495559726. Since the solution to 59 from 4.6 chapter was answered, more than 211 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 72 chapters, and 3369 solutions. The answer to “Ornithologists have determined that some species of birds tend to avoid ights over large bodies of water during daylight hours. It is believed that more energy is required to y over water than over land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 5 km from the nearest point on a straight shoreline, ies to a point on the shoreline, and then ies along the shoreline to its nesting area . Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points and are 13 km apart. (a) In general, if it takes 1.4 times as much energy to y over water as it does over land, to what point should the bird y in order to minimize the total energy expended in returning to its nesting area? (b) Let and L denote the energy (in joules) per kilometer own over water and land, respectively. What would a large value of the ratio WL mean in terms of the birds ight? What would a small value mean? Determine the ratio corresponding to the minimum expenditure of energy. (c) What should the value of be in order for the bird to y directly to its nesting area ? What should the value of be for the bird to y to and then along the shore to ? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 4 km from B, how many times more energy does it take a bird to y over water than over land?” is broken down into a number of easy to follow steps, and 275 words. This textbook survival guide was created for the textbook: Single Variable Calculus: Concepts and Contexts (Stewart's Calculus Series), edition: 4. The full step-by-step solution to problem: 59 from chapter: 4.6 was answered by , our top Calculus solution expert on 03/05/18, 08:43PM.

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Ornithologists have determined that some species of birds tend to avoid ights over large

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