Explanation Given: Given an observer watches a plane approach at a speed of 500 mi / h and altitude of 3 m i and the horizontal distance between the plane and the observer is 4 mi . Concept Used: Theangle of elevation is the angle between a horizontal line from the observer and the line of sight to an object that is above the horizontal line. Calculation: Let x denote the horizontal distance between the plane and the observer as shown in the figure. The height of the observer is insignificant when compared to the height of the plane. Then the angle of observation θ can be modeled by cot θ = x 3 ⇒ θ = cot − 1 ( x 3 ) ⇒ d θ d t = − 1 1 + ( x 3 ) 2 ⇒ d θ d t = − 9 x 2 + 9 d x d t ......... ( 1 ) When x = 4 then d x d t = 500 mi / h

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Chapter 3.7, Problem 52PS

To determine

To find: the rate at which the angle of elevation of the observer’s line of sight changing with respect to time when the horizontal distance between the plane and the observer is 4 mi .

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Chapter 3.7, Problem 51PS

Chapter 3.7, Problem 53PS

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Chapter 3 Solutions

Calculus

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the rate at which the angle of elevation of the observer’s line of sight changing with respect to time when the horizontal distance between the plane and the observer is 4 mi .

Solution Summary: The author analyzes the rate at which the angle of elevation of the observer’s line of sight changing with respect to time.

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To find: the rate at which the angle of elevation of the observer’s line of sight changing with respect to time when the horizontal distance between the plane and the observer is 4 mi .

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Chapter 3 Solutions