AP Calculus ABmediummcq1 pt

A man 6 feet tall walks away from a 15-foot streetlight at 5 ft/s. How fast is the tip of his shadow moving?

5

ft/s

\dfrac{10}{3}

ft/s

15

ft/s

\dfrac{25}{3}

ft/s

Explanation

Core Concept

Similar triangles give $\dfrac{x+s}{15}=\dfrac{s}{6}$ , so $s=\dfrac{2}{3}x$ and the tip is at $x+s=\dfrac{5}{3}x$ . Differentiating gives $\dfrac{d}{dt}(x+s)=\dfrac{5}{3}(5)=\dfrac{25}{3}$ ft/s.

Correct Answer

D $\dfrac{25}{3}$ ft/s

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