Answer
$0.6$ $m/s$
Work Step by Step
$\frac{8}{12}$ = $\frac{2}{y}$
$y$ = $3$ $meters$
If we consider the distance of the man from the building as $x$ then the distance from the spotlight to the man is $12-x$
$\frac{12-x}{12}$ = $\frac{2}{y}$
$1-\frac{1}{12}x$ = $2(\frac{1}{y})$
derivatives both side
$-\frac{1}{12}dx$ = $-2(\frac{1}{y^{2}})dy$
divide by $dt$ both side
$-\frac{1}{12}\frac{dx}{dt}$ = $-2(\frac{1}{y^{2}})\frac{dy}{dt}$
$\frac{dx}{dt}$ = $1.6$ $m/s$
$y$ = $3$
so
$-\frac{1}{12}(1.6)$ = $-2(\frac{1}{3^{2}})\frac{dy}{dt}$
$\frac{dy}{dt}$ = $0.6$ $m/s$
