Answer
0.9 m/s
Work Step by Step
The goal is to find $\frac{dx}{dt}$ at $h=3\,m$.
We are given that $\frac{dh}{dt}= -1.2\,m/s$
Using Pythagoras' theorem, we have
$h^{2}+x^{2}=5^{2}$
Differentiating both sides with respect to $t$, we have
$2h\frac{dh}{dt}+2x\frac{dx}{dt}=0$
$\implies \frac{dx}{dt}=-\frac{h}{x}\frac{dh}{dt}$
When $h=3\,m$, $x=\sqrt {5^{2}-3^{2}}=4\,m$
$\implies \frac{dx}{dt}|_{h=3\,m}=-\frac{3}{4}\times-1.2\,m/s$
$=0.9\,m/s$
