Mathematics - Application of Derivative Question with Solution | TestHub

Let L be the lamp, PQ the man, $OQ=x$ metre his shadow and $MQ=y$ metre the man's distance from the lamp post; $\frac{dy}{dt}=3\mathrm{m}/\mathrm{s}$ (given) $\because △OPQ$ and $△OLM$ are similar: $\frac{OM}{OQ}=\frac{LM}{PQ}\Rightarrow \frac{x+y}{x}=\frac{5}{2}\Rightarrow y=\frac{3}{2}x$ $\therefore \frac{dy}{dt}=\frac{3}{2}\frac{dx}{dt}\Rightarrow 3=\frac{3}{2}\frac{dx}{dt}\Rightarrow \frac{dx}{dt}=2\mathrm{m}/\mathrm{s}$