Solved: Watching a Ferris wheel An observer stands 20 m

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Problem 43E Chapter 4.4

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 43E

Watching a Ferris wheel An observer stands 20 m from the hot tom of a Ferris wheel on a line that is perpendicular to the 1 the wheel, with her eves at the level of the bottom of the wheel. The wheel revolves at a rate of ? rad/min and the observer's line of Sight with a specific seat on the Ferris wheel makes a?n angle ?? with the horizontal (see figure). At what time during a full revo? lution is ?? changing most rapidly?

Step-by-Step Solution:

Solution 43E Step 1: Consider that an observer stands 20 m from the bottom of the Ferris wheel on a line that is perpendicular to the face of the wheel. Consider the line with observer sight and a seat makes angle and the line length is L m. Now, consider the diameter of the wheel is r m. Also, consider that the radius of the wheel is r m. Now, the revolving rate is So, the height of the seat from the ground is: Here t is the time in minute. Draw the wheel accordingly Step 2 Now, the height is also described as sin = h L h = Lsin So, compare with Lsin = r + r sin 2t Find the derivative as L cos d = r(2)cos (2t) dt Also, from the diagram you get cos = 20 L L = 20 cos d Put this intoL cos dt = r(2)cos (2t) 20 d cos os dt= r(2)cos (2t) r(2)cos (2t) dt = 20 d rcos (2t) dt = 10 So, the change of is expressed as d= rcos (2t) dt 10

Step 3 of 4

Chapter 4.4, Problem 43E is Solved
Step 4 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

The full step-by-step solution to problem: 43E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: wheel, ferris, observer, line, most. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Watching a Ferris wheel An observer stands 20 m from the hot tom of a Ferris wheel on a line that is perpendicular to the 1 the wheel, with her eves at the level of the bottom of the wheel. The wheel revolves at a rate of ? rad/min and the observer's line of Sight with a specific seat on the Ferris wheel makes a?n angle ?? with the horizontal (see figure). At what time during a full revo? lution is ?? changing most rapidly?” is broken down into a number of easy to follow steps, and 85 words. Since the solution to 43E from 4.4 chapter was answered, more than 276 students have viewed the full step-by-step answer.

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