The tip of the shadow is moving at [tex]4.8\frac{ft}{sec}[/tex]
Consider the image , as depicted below
Based on similar triangle , we have
[tex]\frac{s(t)}{6} =\frac{s(t)+w(t)}{16}[/tex]
⇒ 10s(t) = 6w(t)
⇒ w(t) = [tex]\frac{10}{6} s(t)[/tex]
we are told that a certain time t,
[tex]\frac{d(w(t))}{dt} = 8\frac{ft}{sec}[/tex]
[tex]\frac{d(w(t))}{dt} = \frac{d(\frac{10}{6}.s(t)) }{dt}[/tex]
[tex]= \frac{10}{6}\frac{d(s(t))}{dt}[/tex]
Therefore,
[tex]\frac{10}{6} \frac{d(s(t))}{dt} = 8\frac{ft}{sec}[/tex]
[tex]\frac{d(s(t))}{dt} = 4.8\frac{ft}{sec}[/tex]
Hence, The tip of the shadow is moving at [tex]4.8\frac{ft}{sec}[/tex]
Learn more about Implicit Differentiation at
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