3. A streetlight is 6 meters above the ground. A person who is 1.5m tall is currently standing an unknown distance away from the streetlight and casting a shadow along the ground. The person starts wallking toward the streetlight at a rate of 1m/s. How fast is the length of the shadow shrinking? Does it depend on how far the person is standing from the streetlight? (a) Draw a diagram showing the situation. (Similar triangles are involved.) (b) Using related rates, determine how fast the length of the person's shadow is shrinking. (Hint: Let x be the distance that the person is from the streetlight, and s be the length of the person's shadow. Use similar triangles to set up an equation between ¤ and s.) Give your answer as a concluding sentence, with correct units. Note: It is possible to get the answer without knowing the distance the person is standing. The answer does not depend on the current value of T.
3. A streetlight is 6 meters above the ground. A person who is 1.5m tall is currently standing an unknown distance away from the streetlight and casting a shadow along the ground. The person starts wallking toward the streetlight at a rate of 1m/s. How fast is the length of the shadow shrinking? Does it depend on how far the person is standing from the streetlight? (a) Draw a diagram showing the situation. (Similar triangles are involved.) (b) Using related rates, determine how fast the length of the person's shadow is shrinking. (Hint: Let x be the distance that the person is from the streetlight, and s be the length of the person's shadow. Use similar triangles to set up an equation between ¤ and s.) Give your answer as a concluding sentence, with correct units. Note: It is possible to get the answer without knowing the distance the person is standing. The answer does not depend on the current value of T.
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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Transcribed Image Text:3. A streetlight is 6 meters above the ground. A person who is 1.5m tall is currently standing an unknown
distance away from the streetlight and casting a shadow along the ground. The person starts walking
toward the streetlight at a rate of 1m/s. How fast is the length of the shadow shrinking? Does it depend
on how far the person is standing from the streetlight?
(a) Draw a diagram showing the situation. (Similar triangles are involved.)
(b) Using related rates, determine how fast the length of the person's shadow is shrinking. (Hint: Let
x be the distance that the person is from the streetlight, and s be the length of the person's shadow.
Use similar triangles to set up an equation between ¤ and s.) Give your answer as a concluding
sentence, with correct units.
Note: It is possible to get the answer without knowing the distance the person is standing. The
answer does not depend on the current value of T.
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