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A street light mounted at the top of a $ 15-ft-tall $ pole. A man $ 6 ft $ tall walks away from the pole with a speed of $ 5 ft/s $ along a straight path. How fast is the tip of his shadow moving when he is $ 40 ft $ from the pole?

(a) What quantities are given in the problem?

(b) What is the unknown?

(c) Draw a picture of the situation for any time $ t. $

(d) Write an equation that relates the quantities.

(e) Finish solving the problem.

a) $15 \mathrm{ft}, 6 \mathrm{ft}, \quad 5 \mathrm{ft} / \mathrm{s}, 40 \mathrm{ft}$

b) The rate that the tip of the man's shadow is moving when he is 40 ft from the pole

c) See step for answer

d) $\frac{6}{15}$

e) $\frac{25}{3} \mathrm{ft} / \mathrm{s}$

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Campbell University

Oregon State University

University of Nottingham

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