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EXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on th path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path. We are given that dat = 4 ft/s and are asked to find der when x = 8. The equation that relates x a A can be written from the figure: tan A Video Example 0 tan A Tutorial Online Textbook Differentiating each side with respect to t, we get dx dA .- 6 sec'(A) · dt dt so dA 1 dx *(4) dt dt cos°(A) When x = 8, the length of the beam is 10, so cos(A) - 10 = and dA dt The searchlight is rotating at a rate of rad/s.

EXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on th path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path. We are given that dat = 4 ft/s and are asked to find der when x = 8. The equation that relates x a A can be written from the figure: tan A Video Example 0 tan A Tutorial Online Textbook Differentiating each side with respect to t, we get dx dA .- 6 sec'(A) · dt dt so dA 1 dx *(4) dt dt cos°(A) When x = 8, the length of the beam is 10, so cos(A) - 10 = and dA dt The searchlight is rotating at a rate of rad/s.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.2: Graphs
Problem 19E
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EXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path. We are given that de = 4 ft/s and are asked to find d/at when x = 8. The equation that relates x and A can be written from the figure: - tan A Video Example ) tan A Tutorial Online Textbook Differentiating each side with respect to t, we get dx dA -- 6 sec'(A) dt dt so dA 1 dx 1 *(4) dt 6 dt 6 cos (A) When x = 8, the length of the beam is 10, so cos(A) = /10 = and dA dt The searchlight is rotating at a rate of rad/s.
Transcribed Image Text:EXAMPLE 5 A man walks along a straight path at a speed of 4 ft/s. A searchlight is located on the ground 6 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 8 ft from the point on the path closest to the searchlight? SOLUTION We draw the figure to the left and let x be the distance from the man to the point on the path closest to the searchlight. We let A be the angle between the beam of the searchlight and the perpendicular to the path. We are given that de = 4 ft/s and are asked to find d/at when x = 8. The equation that relates x and A can be written from the figure: - tan A Video Example ) tan A Tutorial Online Textbook Differentiating each side with respect to t, we get dx dA -- 6 sec'(A) dt dt so dA 1 dx 1 *(4) dt 6 dt 6 cos (A) When x = 8, the length of the beam is 10, so cos(A) = /10 = and dA dt The searchlight is rotating at a rate of rad/s.
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