A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight

Question

A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 35 ft from the pole?

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RI SƠ 3 years 2021-08-15T23:25:51+00:00 1 Answers 18 views 0

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  1. bonexptip
    0
    2021-08-15T23:27:10+00:00
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    Answer:

    Explanation:

    height of pole = 15 ft

    height of man = 6 ft

    Let the length of shadow is y .

    According to the diagram

    Let at any time the distance of man is x.

    The two triangles are similar

    \frac{y-x}{y}=\frac{6}{15}

    15 y – 15 x = 6 y

    9 y = 15 x

    y=\frac{5}{3}x

    Differentiate with respect to time.

    \frac{dy}{dt}=\frac{5}{3}\frac{dx}{dt}

    As given, dx/dt = 4 ft/s

    \frac{dy}{dt}=\frac{5}{3}\times 4

    \frac{dy}{dt}=\frac{20}{3} ft/s

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