Answer:
2.5 ft/s
Step-by-step explanation:
[tex]\dfrac{dx}{dt}=\text{Speed of person}=3\ \text{ft/s}[/tex]
As the triangles are similar we have
[tex]\dfrac{y}{6}=\dfrac{20}{12}\\\Rightarrow y=6\times\dfrac{5}{3}=10[/tex]
Again from the similar triangles we get
[tex]\dfrac{y}{6}=\dfrac{20}{20-x}\\\Rightarrow (20-x)y=120\\\Rightarrow x=20-\dfrac{120}{y}[/tex]
Differentiating with respect to time we get
[tex]\dfrac{dx}{dt}=\dfrac{120}{y^2}\dfrac{dy}{dt}\\\Rightarrow 3=\dfrac{120}{10^2}\dfrac{dy}{dt}\\\Rightarrow \dfrac{dy}{dt}=\dfrac{3}{1.2}\\\Rightarrow \dfrac{dy}{dt}=2.5\ \text{ft/s}[/tex]
The rate of change of the length of the shadow on the wall is 2.5 ft/s.
