Chapter 2.8, Problem 49E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A runner sprints around a circular track of radius 100 m at a constant speed of 7 m/s. The runner’s friend is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200 m?

To determine

**To find:**

How fast is the distance between the friends changing?

Explanation

**1. Formula:**

i. Arc length

ii. Law of cosine:

**2. Given:**

Radius of circular track =

The figure is as shown below.

**3. Calculations:**

Using arclength formula,

Differentiate it.

Substituting

Using cosine rule

Differentiate it with respect to t

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