Explanation Given: Length of the ladder, L =5 m Time, t = 2 s. Let, h be the height of the top of the ladder in m x be the distance between the base of the ladder and the wall v be the speed of the top and base of the ladder The derivatives of the functions with respect to time must be equal since the top and base of the ladder are moving at the same speed. And also the ladder is moving. So the velocity cannot be zero. That means, d x d t = − d h d t = − v According to the Pythagorean Theorem, h 2 + x 2 = 5 2 Differentiating the above equation with respect to time t, we get 2 h d h d

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 3.9, Problem 12E

To determine

To find out the relationship between h and x when the top base of the ladder at move at the same speed.

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Chapter 3.9, Problem 11E

Chapter 3.9, Problem 13E

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Chapter 3 Solutions

Calculus - Standalone book

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To find out the relationship between h and x when the top base of the ladder at move at the same speed.

Solution Summary: The author explains that the relationship between h and x is given by (h = v) when the top base of the ladder at move at the same speed.

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To find out the relationship between h and x when the top base of the ladder at move at the same speed.

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Chapter 3 Solutions