Chapter 2.R, Problem 79E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 s later?

To determine

**To find:**

How fast is the distance between the boy and the balloon increasing 3 s later

Explanation

**1. Concept:**

Use differentiation

**2. Formula:**

i. Power rule:

ii. Difference rule:

iii. Chain rule:

**3. Given:**

4. **Calculation:**

The relation between h, x, and s is

Differentiate with respect to t on both sides

Therefore,

By using sum rule

By using power rule and chain rule

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