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A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 40 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, a the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express as a function of x. 0 = tan (20/x) (b) What is the value of at the moment in question? Give the exact value. x = 20*sqrt(3) (c) What is the value of do dt = rad -1/60 sec(1/sqrt(3))^2 m do at the same moment? Give the exact value, paying attention to the sign. dt rad/s

A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 40 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, a the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express as a function of x. 0 = tan (20/x) (b) What is the value of at the moment in question? Give the exact value. x = 20*sqrt(3) (c) What is the value of do dt = rad -1/60 sec(1/sqrt(3))^2 m do at the same moment? Give the exact value, paying attention to the sign. dt 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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A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 40 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express as a function of a. 0 = tan (20/x) (b) What is the value of at the moment in question? Give the exact value. x = 20*sqrt(3) (c) What is the value of de dt rad -1/60 sec(1/sqrt(3))^2 m do at the same moment? Give the exact value, paying attention to the sign. dt rad/s
Transcribed Image Text:A kite glides horizontally at an altitude of 20 m while we unspool the string. Consequently, the angle made between the string and the horizon diminishes. We would like to determine the rate at which this angle decreases once 40 m of string has been unspooled, given that, at that instant, the kite's horizontal velocity is 1 m/s. To solve this problem, let be the angle in radians made between the string and the horizontal, the kite's horizontal position in meters since being attached to the ground, and t the time in seconds. We further suppose that the string is straight and taut. (a) Sketch a diagram of this question and use it to express as a function of a. 0 = tan (20/x) (b) What is the value of at the moment in question? Give the exact value. x = 20*sqrt(3) (c) What is the value of de dt rad -1/60 sec(1/sqrt(3))^2 m do at the same moment? Give the exact value, paying attention to the sign. dt rad/s
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