Answer
0.675 m/s
Work Step by Step
Distance $x= velocity\times time= (1.2 \,m/s)t$
From the two similar triangles in the figure, we can write
$\frac{5}{height\,of\,man}=\frac{x+y}{y}$
$\implies \frac{5}{1.8}=\frac{1.2\,t+y}{y}$
$\implies 2.777778=\frac{1.2\,t}{y}+1$
$\implies 1.777778= \frac{1.2\,t}{y}$
Or,
$y= \frac{1.2\,t}{1.777778}=0.675\,t$
Hence, the rate at which the shadow is increasing is:
$\frac{dy}{dt}=0.675\,m/s$
