A police car is moving north towards an intersection at 24 miles per hour, and the police inside the car is using radar to determine the rate at which the distance is changing between them and another vehicle that is traveling west. When the police car is 3 miles south of the intersection and the other vehicle is 4 miles west of the intersection, it is determined that the distance between them and the other vehicle is increasing at a rate of 20 miles per hour. Find the speed of the car when the car is 4 miles west of the intersection.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Can I get some help with this word problem?
Assignment: Complete the following related rates word problem. Include a well-labeled
figure and supporting mathematical statements within a grammatically correct exposition.
A police car is moving north towards an intersection at 24 miles per hour, and the police
inside the car is using radar to determine the rate at which the distance is changing between
them and another vehicle that is traveling west. When the police car is 3 miles south of the
intersection and the other vehicle is 4 miles west of the intersection, it is determined that
the distance between them and the other vehicle is increasing at a rate of 20 miles per hour.
Find the speed of the car when the car is 4 miles west of the ìntersection.
Transcribed Image Text:Assignment: Complete the following related rates word problem. Include a well-labeled figure and supporting mathematical statements within a grammatically correct exposition. A police car is moving north towards an intersection at 24 miles per hour, and the police inside the car is using radar to determine the rate at which the distance is changing between them and another vehicle that is traveling west. When the police car is 3 miles south of the intersection and the other vehicle is 4 miles west of the intersection, it is determined that the distance between them and the other vehicle is increasing at a rate of 20 miles per hour. Find the speed of the car when the car is 4 miles west of the ìntersection.
Expert Solution
Step 1

Given: 

         Speed of the police car, dydt = 24 miles/hour (positive moving towards + y axis)

         Speed of car with respect to other vehicles moving west, dcdt = - 20 miles/hour (negative moving towards - x axis)

         Distance of police car from the intersection, y = -3 miles (OA)

         Distance of other vehicle from the intersection, x = - 4 miles (OB)

Determine the speed of the car, dxdt.  

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