Mathematics: A street light is mounted at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35 ft from the base of the pole

3.60285 is ur answer hope this helped!...

A street light is mounted at the top of a 12 ft

skylar7192

06.02.2022

16 ft/s.

Step-by-step explanation:

$\dfrac{dx}{dt}=\text{Velocity of person}=8\ \text{ft/s}$

As the two triangles in the figure are similar to each other we have

$\dfrac{12}{y}=\dfrac{6}{y-x}\\\Rightarrow \dfrac{2}{y}=\dfrac{1}{y-x}\\\Rightarrow 2y-2x=y\\\Rightarrow y-2x=0\\\Rightarrow y=2x$

Differentiating with respect to time we have

$\dfrac{dy}{dt}=2\dfrac{dx}{dt}\\\Rightarrow \dfrac{dy}{dt}=2\times8\\\Rightarrow \dfrac{dy}{dt}=16\ \text{ft/s}$

Rate at which the tip of the shadow moves away from the pole is 16 ft/s.

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