Chapter 2.8, Problem 30E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

To determine

**To find:**

The rate at which the angle between the string and horizontal isdecreasing.

Explanation

**1. Concept:**

We can plot the figure from the given situation and then use the trigonometric ratio and differentiation to find the rate of change of angle.

**2. Formula:**

i.

ii. Derivative of cotangent:

iii. Chain rule of differentiation:

**3. Given:**

The kite is

**4. Calculations:**

Differentiate it with respect to t

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