Answered: A car traveling south towards Sioux…

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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A car traveling south towards Sioux Falls at 160 km/hr is chasing a truck traveling east away from Sioux Falls at 140 km/hr. At time t = 0, the car is 20 km north of Sioux Falls and the truck is 30 km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing at time t= 0 and then five minutes later.

Expert Solution

Step 1

Given, A car traveling south towards Sioux Falls at 160 km/hr is chasing a truck traveling east away from Sioux Falls at 140 km/hr.

Let the distance of the car and the truck from Sioux Falls be 'x' and 'y' and the distance between the vehicles be 'S'

At time t=0,

x = 20km and y = 30km

$∴ S = \sqrt{x^{2} + y^{2}} = > S = \sqrt{20^{2} + 30^{2}} = > S = 10 \sqrt{13} Km$

$\frac{dx}{dt} = - 160 km / hr (negative because x is decreasing) \frac{dy}{dt} = 140 km / hr$

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