   Chapter 11.4, Problem 33E ### 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

# Ladder safety A 30-ft ladder is leaning against a wall. If the bottom is pulled away from the wall at a rate of 1 ft/sec, at what rate is the top of the ladder sliding down the wall when the bottom is 18 ft from the wall?

To determine

To calculate: The rate at which the top of the ladder is sliding down the wall when the bottom is 18 ft from the wall if a 30-ft ladder is leaning against a wall and the bottom is pulled away from the wall at a rate of 1-ft/sec.

Explanation

Given Information:

A 30-ft ladder is leaning against a wall and the bottom is pulled away from the wall at a rate of 1-ft/sec.

Formula used:

According to the Pythagoras theorem,

a2+b2=c2

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

Calculation:

As it is provided that a 30-ft ladder is leaning against a wall and the bottom is pulled away from the wall at a rate of 1-ft/sec.

Thus, this arrangement can be considered as a right angled triangle with the length of the ladder be the hypotenuse of the triangle and the height of the wall be the height of triangle.

Now, x be the height of the wall and y be the horizontal distance from the ladder to the wall, then, according to the Pythagoras theorem,

302=x2+y2 …… (1)

Differentiate the above equation with respect to t as,

0=2xdxdt+2ydydt …… (2)

Now, the rate at which the top of the ladder is sliding down the wall when the bottom is 18 ft from the wall is to be obtained, so substitute

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