Answer
$x=4.737\,m$
$\frac{dx}{dt}=0.405\,m/s$
Work Step by Step
$h(2)=h(0)+ dt\times\frac{dh}{dt}$
$=4\,m+(2\,s\times-1.2\,m/s)=1.6\,m$
As $x^{2}+h^{2}=5^{2}$,
$x(2)=\sqrt {(5\,m)^{2}-(1.6\,m)^{2}}=4.737\,m$
Differentiating both sides of the equation $x^{2}+h^{2}=5^{2}$ with respect to $t$, we have
$2x\frac{dx}{dt}+2h\frac{dh}{dt}=0$
$\implies \frac{dx}{dt}=-\frac{h}{x}\frac{dh}{dt}$
$\frac{dx}{dt}|_{t=2\,s}=-\frac{1.6\,m}{4.737\,m}\times(-1.2\,m/s)=0.405\,m/s$
