Question

A man 6ft tall walks at the rate of 5ft/sec toward a streetlight that is 16ft above the ground. At what rate is the tip of his shadow moving? B. At what rate is the length of his shadow changing when he is 10 ft from the base of the light?

Answer 1

A. Is the first question...

Answer 2

So lets find length of the shadow,'s', when he is 'd' ft away
by similar triangle we get this proportion
\[\frac{16}{d+s}=\frac{6}{s}\]
\[16s=6d+6s\]
\[s=\frac{6}{10}d\]
\[\frac{\text{ds}}{\text{dt}}=\frac{6}{10}\frac{\text{dD}}{\text{dt}}\]
Given Info
\[\frac{\text{dD}}{\text{dt}}=5\]