   Chapter 2.8, Problem 30E

Chapter
Section
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:

ddx(cotx)= -csc2x

iii. Chain rule of differentiation:

ddtfx=ddxfx*dxdt

3. Given:

The kite is 100 ft above the ground.dxdt=8 ft/s

4. Calculations:

cotθ=x100

Differentiate it with respect to t

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