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Calculus / Calculus: Early Transcendentals 1 / Chapter 4.4 / Problem 42E

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

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Searchlight problem—narrow beam A searchlight is 100 in

Chapter 7, Problem 42E

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QUESTION:

A searchlight is 100 m 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 \(\pi / 6\) rad/s, find the rate at which the beam sweeps along the highway as a function of \(\theta\). For what value of \(\theta\) is this rate minimized?

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QUESTION:

A searchlight is 100 m 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 \(\pi / 6\) rad/s, find the rate at which the beam sweeps along the highway as a function of \(\theta\). For what value of \(\theta\) is this rate minimized?

ANSWER:

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

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