A man is walking towards a vertical pillar in a straight path, at a uniform speed.

Question

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30o. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60o. Then the time taken (in minutes) by him, from B to reach the pillar, is :

Accepted Answer

According to given information, we have the following figure

Now, from $	riangle A C D$ and $	riangle B C D$, we have

$	an 30^{\circ}=\frac{h}{x+y}$

and $	an 60^{\circ}=\frac{h}{y}$

$\Rightarrow h=\frac{x+y}{\sqrt{3}}\quad...(i)$

and $h=\sqrt{3} y\quad...(ii)$

From Eqs. (i) and (ii),

$\frac{x+y}{\sqrt{3}}=\sqrt{3} y \Rightarrow x+y=3 y$

$\Rightarrow x-2 y=0 \Rightarrow y=\frac{x}{2}$

$\because$ Speed is uniform.

$	herefore$ Distance $y$ will be cover in $5 \mathrm{~min}$.

$\because$ Distance $x$ covered in $10 \mathrm{~min}$.

$	herefore$ Distance $\frac{x}{2}$ will be cover in $5 \mathrm{~min}$.

Solutions · 1