A man of height h walks in a straight path towards lamp post of height $H$ with velocity $v$. Then velocity…

A man of height h walks in a straight path towards lamp post of height $H$ with velocity $v$. Then velocity of the edge of the shadow on the ground will be
  1. $\frac{\mathrm{h} v}{\mathrm{H}+\mathrm{h}}$
  2. $\frac{\mathrm{H} v}{\mathrm{H}-h}$
  3. $\frac{\mathrm{H}+h}{\mathrm{H} v}$
  4. $\frac{(\mathrm{H}-h)}{\mathrm{H} h}$

Solution

as $\Delta \mathrm{LOS}$ and $\Delta \mathrm{MPS}$ are similar so, $\frac{\mathrm{H}}{x}=\frac{\mathrm{h}}{x-y} \Rightarrow(\mathrm{H}-\mathrm{h}) x=\mathrm{Hy}$
$\Rightarrow(\mathrm{H}-\mathrm{h}) \frac{\mathrm{dx}}{\mathrm{dt}}=\mathrm{H} \frac{\mathrm{dy}}{\mathrm{dt}}=\mathrm{Hv}$
$\Rightarrow \mathrm{V}_{\mathrm{s}}=\frac{\mathrm{Hv}}{\mathrm{H}-\mathrm{h}}$

Asked in: JEE Mains - Motion In One Dimension - Test 1

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