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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20 cosh(x/20) – 15, where x and y are measured in meters.

(a) Find the slope of this curve where it meets the right pole.

(b) Find the angle θ between the line and the pole.

Chapter 3.11, Problem 51E, A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20 cosh(x/20)

(a)

To determine

To find: The slope of the given curve where it meets the right pole.

Explanation

Given:

The distance between two poles is 14 m,

The telephone line is hangs between two poles,

The shape of the catenary is y=20cosh(x20)15.

Formula used:

The hyperbolic functions ddx(coshx)=sinhx.

Calculation:

From given graph, it is observed that the right pole located at 7 in x axis.

Obtain the derivative of y=20cosh(x20)15 at x = 7.

dydx=ddx(20cosh(x20)15)=ddx(20cosh(x20))ddx(15)=20ddx(cosh(x20))0=20ddx(cosh

(b)

To determine

To find: The angle θ between line and pole.

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