   Chapter 11.4, Problem 34E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Flight A kite is 30 ft high and is moving horizontally at a rate of 10 ft/min. If the kite string is taut, at what rate is the string being played out when 50 ft of string is out?

To determine

To calculate: The rate at which the string is being played out when 50 ft of string is out, if a kite is 30 ft high and is moving horizontally at a rate of 10 ft/min.

Explanation

Given Information:

A kite is 30 ft high and is moving horizontally at a rate of 10 ft/min.

Formula used:

According to the Pythagoras theorem,

a2+b2=c2

Where a,b,c are the sides of the triangle.

According to the chain rule differentiation, if y=f(u), where u=g(x), then y is a differentiable function of x.

dydx=dydududx

The derivative of a constant value, k, is

ddx(k)=0

According to the sum rule of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

Calculation:

As it is provided that a kite is 30 ft high and is moving horizontally at a rate of 10ft/min.

Thus, this arrangement can be considered as a right angled triangle with the length of the string be the hypotenuse of the triangle and the horizontal distance be the base and height of the kite be the altitude/height of the triangle

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