A kite 100ft above the ground moves horizontally at a speed of 2ft/s. At what rate is the angle between the string and the horizontal decreasing when 250ft of string has been let out? Answer (in radians per second):
A kite 100ft above the ground moves horizontally at a speed of 2ft/s. At what rate is the angle between the string and the horizontal decreasing when 250ft of string has been let out? Answer (in radians per second):
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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![**Problem Statement:**
A kite 100 ft above the ground moves horizontally at a speed of 2 ft/s. At what rate is the angle between the string and the horizontal decreasing when 250 ft of string has been let out?
**Answer Section:**
Enter your answer (in radians per second):
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**Explanation:**
This problem involves related rates, where you are tasked with finding the rate of change of the angle between the kite string and the horizontal plane. You are given:
1. The vertical height of the kite is constant at 100 ft.
2. The kite moves horizontally at 2 ft/s.
3. The string length is 250 ft at the moment of interest.
Using trigonometric relationships and calculus, specifically the concept of related rates, you can solve for the rate at which the angle is decreasing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc84364e-ef46-429b-9d16-57e28333362b%2Fdff8f641-0111-45a2-99a8-2ca7a2d0f153%2F5s15xfd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A kite 100 ft above the ground moves horizontally at a speed of 2 ft/s. At what rate is the angle between the string and the horizontal decreasing when 250 ft of string has been let out?
**Answer Section:**
Enter your answer (in radians per second):
[Answer Box]
**Buttons:**
- Preview My Answer
- Submit Answer
**Explanation:**
This problem involves related rates, where you are tasked with finding the rate of change of the angle between the kite string and the horizontal plane. You are given:
1. The vertical height of the kite is constant at 100 ft.
2. The kite moves horizontally at 2 ft/s.
3. The string length is 250 ft at the moment of interest.
Using trigonometric relationships and calculus, specifically the concept of related rates, you can solve for the rate at which the angle is decreasing.
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