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Example 5 Video Example 4O A man walks along a straight path at a speed of 5 ft/s. A searchlight is located on the ground 12 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight? Solution We draw the figure below and let x be the distance from the man to the point on the path closest to the searchlight. We let e be the angle between the beam of the searchlight and the perpendicular to the path. 12 dx We are given that X-5 ft/s and are asked to find 00 when x- 5. The equation that relates x and e can be written from the figure. dt dt x - ( 12 tan(0). - tan(0) 12 Differentiating each side with respect to t, we get so (5) When x - 5, the length of the beam is 13, so cos(0) - and The searchlight is rotating at a rate of rad/s.

Example 5 Video Example 4O A man walks along a straight path at a speed of 5 ft/s. A searchlight is located on the ground 12 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight? Solution We draw the figure below and let x be the distance from the man to the point on the path closest to the searchlight. We let e be the angle between the beam of the searchlight and the perpendicular to the path. 12 dx We are given that X-5 ft/s and are asked to find 00 when x- 5. The equation that relates x and e can be written from the figure. dt dt x - ( 12 tan(0). - tan(0) 12 Differentiating each side with respect to t, we get so (5) When x - 5, the length of the beam is 13, so cos(0) - and The searchlight is rotating at a rate of rad/s.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Example 5 Video Example ) A man walks along a straight path at a speed of 5 ft/s. A searchlight is located on the ground 12 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight? Solution We draw the figure below and let x be the distance from the man to the point on the path closest to the searchlight. We let e be the angle between the beam of the searchlight and the perpendicular to the path. 12 We are given that xp = 5 ft/s and are asked to find . op when x = 5. The equation that relates x and e can be written from the figure. dt dt ) tan(@). tan(0) X = 12 Differentiating each side with respect to t, we get dx de dt dt so xp dt de dt (5) When x = 5, the length of the beam is 13, so cos(0) and OP dt The searchlight is rotating at a rate of rad/s. 12
Transcribed Image Text:Example 5 Video Example ) A man walks along a straight path at a speed of 5 ft/s. A searchlight is located on the ground 12 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 5 ft from the point on the path closest to the searchlight? Solution We draw the figure below and let x be the distance from the man to the point on the path closest to the searchlight. We let e be the angle between the beam of the searchlight and the perpendicular to the path. 12 We are given that xp = 5 ft/s and are asked to find . op when x = 5. The equation that relates x and e can be written from the figure. dt dt ) tan(@). tan(0) X = 12 Differentiating each side with respect to t, we get dx de dt dt so xp dt de dt (5) When x = 5, the length of the beam is 13, so cos(0) and OP dt The searchlight is rotating at a rate of rad/s. 12
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