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A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.15 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.) Cubmit A m/sec

A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank (see figure). Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.15 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.) Cubmit A m/sec

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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Question
**Understanding Rates of Change in Construction** _A construction scenario to illustrate related rates in calculus:_ A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank. Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.15 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.) **Diagram Explanation:** - The diagram depicts a building under construction with a worker pulling a plank up the side. - The plank is 5 meters long. - One end of the plank, attached to a rope, is being pulled vertically. - The other end slides horizontally along the ground. - A right triangle is formed with the wall, the ground, and the plank. - The diagram is annotated to show the plank's length (5 m) and the distance of the sliding end from the wall (1.5 meters). **Answer Submission:** - A text box is provided for users to input the rate at which the end of the plank slides along the ground (in meters per second). - A "Submit Answer" button is included for users to submit their calculations. This problem helps in understanding how the rates of change in different dimensions are related in practical situations, such as construction.
Transcribed Image Text:**Understanding Rates of Change in Construction** _A construction scenario to illustrate related rates in calculus:_ A construction worker pulls a five-meter plank up the side of a building under construction by means of a rope tied to one end of the plank. Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of 0.15 meter per second. How fast is the end of the plank sliding along the ground when it is 1.5 meters from the wall of the building? (Round your answer to two decimal places.) **Diagram Explanation:** - The diagram depicts a building under construction with a worker pulling a plank up the side. - The plank is 5 meters long. - One end of the plank, attached to a rope, is being pulled vertically. - The other end slides horizontally along the ground. - A right triangle is formed with the wall, the ground, and the plank. - The diagram is annotated to show the plank's length (5 m) and the distance of the sliding end from the wall (1.5 meters). **Answer Submission:** - A text box is provided for users to input the rate at which the end of the plank slides along the ground (in meters per second). - A "Submit Answer" button is included for users to submit their calculations. This problem helps in understanding how the rates of change in different dimensions are related in practical situations, such as construction.
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