Answer:
16 ft/s.
Step-by-step explanation:
[tex]\dfrac{dx}{dt}=\text{Velocity of person}=8\ \text{ft/s}[/tex]
As the two triangles in the figure are similar to each other we have
[tex]\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[/tex]
Differentiating with respect to time we have
[tex]\dfrac{dy}{dt}=2\dfrac{dx}{dt}\\\Rightarrow \dfrac{dy}{dt}=2\times8\\\Rightarrow \dfrac{dy}{dt}=16\ \text{ft/s}[/tex]
Rate at which the tip of the shadow moves away from the pole is 16 ft/s.
