A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole? 16/3 X ft/s Enhanced Feedback Please try again. Draw a diagram for this problem. Draw a right triangle with horizontal and vertical edges. Let the vertical edge be the pole. Draw another vertical line with one end on the hypotenuse prizontal odgo donicting Label the distance between the man and the pole x and the distance hetween the man and the tio of the shadow v. Use properties of

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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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 street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft
from the pole?
16/3
X ft/s
Enhanced Feedback
Please try again. Draw a diagram for this problem. Draw a right triangle with horizontal and vertical edges. Let the vertical edge be the pole. Draw another vertical line with one end on the hypotenuse:
and the other end on the horizontal edge depicting the man. Label the distance between the man and the pole x and the distance between the man and the tip of the shadow y. Use properties of
similar triangles to find a relation among x, y, the height of the man, and the height of the pole. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the
rate at which the tip of the shadow is moving, (x + y). Then, use the values from the exercise to evaluate the rate of change of the distance between the tip of the shadow and the pole, paying
dt
clore attention to the signs of the rates of change (positive when increasing, and negative when decreasing).
Transcribed Image Text:A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 30 ft from the pole? 16/3 X ft/s Enhanced Feedback Please try again. Draw a diagram for this problem. Draw a right triangle with horizontal and vertical edges. Let the vertical edge be the pole. Draw another vertical line with one end on the hypotenuse: and the other end on the horizontal edge depicting the man. Label the distance between the man and the pole x and the distance between the man and the tip of the shadow y. Use properties of similar triangles to find a relation among x, y, the height of the man, and the height of the pole. Differentiate this equation with respect to time, t, using the Chain Rule, to find the equation for the rate at which the tip of the shadow is moving, (x + y). Then, use the values from the exercise to evaluate the rate of change of the distance between the tip of the shadow and the pole, paying dt clore attention to the signs of the rates of change (positive when increasing, and negative when decreasing).
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