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Searchlight problem—narrow beam A searchlight is 100 in

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 42E 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 42E

Searchlight problem—narrow beam A searchlight is 100 in from the nearest point on a straight highway (see figure). As it rotates, the searchlight casts a horizontal beam that intersects the highway in a point. If the light revolves at a rate of ? /6 rad/s, find the rate at which the beam sweeps along the highway as a func ? tion of ??. For what? alue of ?? is this rate minimized?

Step-by-Step Solution:

Solution 42E Step 1: Given data S is the searchlight,P is the person and triangle QPS is the right angled triangle The searchlight rotates when the person is 100 meters from the searchlight Angular velocity of the searchlight, dt = 6ad/sec Step 2: From the given data we can draw the following figure

Step 3 of 4

Chapter 4.4, Problem 42E is Solved
Step 4 of 4

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

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