Explanation Given: Stuart is 6 feet tall and is walking towards a 20 foot streetlight at a rate of 4 feet per second. And his shadow gets shorter as he walks towards the streetlight. Concept Used: Corresponding sides of two similar triangles are in same proportion. Calculation: To determine how fast the tip of Stuart’s shadow is changing. First let x be the distance between Stuart and the 20 feet tall streetlight and let s be the length of his shadow, represented by the picture below Then d x d t = − 4 feet per second As given he is walking towards the streetlight at a rate of 4 feet per second negative sign represents that x is getting smaller as Stuart is moving towards streetlight. Now find how fast the length of Stuart’s shadow is changing that is d s / d t . Now, note that the triangles ABC and DEC are similar then according to property of similar triangle ratio of their correspondence sides is equal; that is AB CB = DE CE ⇒ 20 s + x = 6 s ⇒ 20 s = 6 ( s + x ) ⇒ 20 s = 6 s + 6 x ⇒ 6 x = 20 s − 6 s ⇒ 6 x = 14 s ⇒ x = 14 <

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ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 3.5, Problem 47A

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The change in tip of Stuart’s shadow, and does it depend on the distance between Stuart and streetlight.

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Chapter 3.5, Problem 46A

Chapter 3.5, Problem 48A

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The change in tip of Stuart’s shadow, and does it depend on the distance between Stuart and streetlight.

Solution Summary: The author analyzes how the tip of Stuart's shadow is changing at a rate of 407 feet per second.

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