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A bulb is placed at the centre of a circular track of radius $10 \mathrm{~m}$. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of $10 \mathrm{~m} / \mathrm{sec}$. Starting from $\mathrm{P}$ the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ}$ from $P$ is
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$40 \mathrm{~m} / \mathrm{sec}$
$\overrightarrow{\mathrm{v}}=\mathrm{r} \frac{\mathrm{d} \theta}{\mathrm{dt}}=10$
$\tan \theta=\frac{\mathrm{y}}{\mathrm{r}}$ or, $\mathrm{y}=\mathrm{r} \tan \theta$ or, $\frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{r} \sec ^{2} \theta \cdot \frac{\mathrm{d} \theta}{\mathrm{dt}}=10 \times \sec ^{2}\left(60^{\circ}\right)=40 \mathrm{~m} / \mathrm{sec}$
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