Question

Related Rates Problem
A man 6ft tall walks at the rate of 4 ft/sec toward a street light that is 16ft above the ground. At what rate is the length of his shadow changing when he is 7ft from the base of the light?

Answer 1

First, draw a picture and label similar triangle parts.

Answer 2

set up proportion
\[\frac{s}{6} = \frac{x+s}{16}\]
solving for "s"
\[s = \frac{3}{5} x\]
chain rule says
\[\frac{ds}{dt} = \frac{ds}{dx}*\frac{dx}{dt}\]
dx/dt is given as -4 since you are walking towards light, x is decreasing
\[\rightarrow \frac{ds}{dx} = \frac{3}{5}\]
therefore
\[\frac{ds}{dt} = \frac{3}{5}*(-4) = -\frac{12}{5}\]