A kite 100 ft above the ground moves horizontally at a speed of 11 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? -11/400 x rad/s Enhanced Feedback Please try again. Let e be the angle between the string and the ground and x denote the horizontal distance of the kite. Then x is one leg of a right triangle with hypotenuse formed by the string; the other leg is facing th

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 67E
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A kite 100 ft above the ground moves horizontally at a speed of 11 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out?
|-11/400 x rad/s
Enhanced Feedback
Please try again. Let e be the angle between the string and the ground and x denote the horizontal distance of the kite. Then x is one leg of a right triangle with hypotenuse formed by the string; the other leg is facing the angle e and has length equal to the height of
the kite. You need to use a trigonometric function to relate e and x and then differentiate the relation with respect to t. Finally, solve for 20 and find its value using the given values. Note that negative rate means the quantity is decreasing.
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Transcribed Image Text:A kite 100 ft above the ground moves horizontally at a speed of 11 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? |-11/400 x rad/s Enhanced Feedback Please try again. Let e be the angle between the string and the ground and x denote the horizontal distance of the kite. Then x is one leg of a right triangle with hypotenuse formed by the string; the other leg is facing the angle e and has length equal to the height of the kite. You need to use a trigonometric function to relate e and x and then differentiate the relation with respect to t. Finally, solve for 20 and find its value using the given values. Note that negative rate means the quantity is decreasing. dt Need Help? Read It
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