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3. A police officer is sitting 100 feet north of an intersection. He spots a car traveling due east, and triggers the radar detector. This detects the car is exactly 300 feet from the police officer, and is traveling -65 mph. This speed is the how fast the car is moving toward the police officer, but does not represent the speed of the car moving east. This is what we are actually trying to measure. (a) Draw a diagram of the situation on the intersection to the right. Label any distances. (b) Let x be the distance the car is from the intersection, and r be the distance between the cop and the car. Why is x2 + 1002 = 3002 a poor choice for analyzing this problem? (c) Using Geometry, what is the value of x? dx (d) Using x + 1002 = r2, take the time derivative and solve for dt

3. A police officer is sitting 100 feet north of an intersection. He spots a car traveling due east, and triggers the radar detector. This detects the car is exactly 300 feet from the police officer, and is traveling -65 mph. This speed is the how fast the car is moving toward the police officer, but does not represent the speed of the car moving east. This is what we are actually trying to measure. (a) Draw a diagram of the situation on the intersection to the right. Label any distances. (b) Let x be the distance the car is from the intersection, and r be the distance between the cop and the car. Why is x2 + 1002 = 3002 a poor choice for analyzing this problem? (c) Using Geometry, what is the value of x? dx (d) Using x + 1002 = r2, take the time derivative and solve for dt

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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**Problem 3: Related Rates Problem** A police officer is positioned 100 feet north of an intersection. He notices a car traveling due east, which activates the officer's radar detector. The radar indicates that the car is exactly 300 feet away from the police officer and moving at -65 mph. This speed reflects how rapidly the car approaches the police officer, rather than its eastward speed, which is what we are actually aiming to determine. **Tasks:** (a) **Diagram Drawing:** - Draw a diagram representing the situation relative to the intersection. - Label pertinent distances clearly, including the distance from the intersection to the officer and the car. (b) **Distance Analysis:** - Let \( x \) represent the distance from the car to the intersection, and \( r \) the distance between the officer and the car. - Discuss why using \( x^2 + 100^2 = 300^2 \) is not suitable for this analysis. (c) **Geometric Calculation:** - Use geometric principles to determine the value of \( x \). (d) **Differentiation:** - Using \( x^2 + 100^2 = r^2 \), differentiate with respect to time to determine \( \frac{dx}{dt} \).
Transcribed Image Text:**Problem 3: Related Rates Problem** A police officer is positioned 100 feet north of an intersection. He notices a car traveling due east, which activates the officer's radar detector. The radar indicates that the car is exactly 300 feet away from the police officer and moving at -65 mph. This speed reflects how rapidly the car approaches the police officer, rather than its eastward speed, which is what we are actually aiming to determine. **Tasks:** (a) **Diagram Drawing:** - Draw a diagram representing the situation relative to the intersection. - Label pertinent distances clearly, including the distance from the intersection to the officer and the car. (b) **Distance Analysis:** - Let \( x \) represent the distance from the car to the intersection, and \( r \) the distance between the officer and the car. - Discuss why using \( x^2 + 100^2 = 300^2 \) is not suitable for this analysis. (c) **Geometric Calculation:** - Use geometric principles to determine the value of \( x \). (d) **Differentiation:** - Using \( x^2 + 100^2 = r^2 \), differentiate with respect to time to determine \( \frac{dx}{dt} \).
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