Question

A peacock is sitting on the top of a tree. It observes a serpent on the ground making an angle of depression of ${30}^{\circ }$. The peacock with the speed of 400 m/min catches the serpent in 15 seconds. Find the height of the tree.

• A. $\frac{80}{\sqrt{3}}m$
• B. $80\sqrt{3}m$
• C. $100\sqrt{3}m$
• D. $\frac{100}{\sqrt{3}}m$

Answer 1

The correct option is D $\frac{100}{\sqrt{3}}m$

Let Peacock be at point B and AB be the height of the tree whereas C be the point where Serepent is.

Given speed = 400 m/min
We know, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
So, Distance = AC = Speed × Time
$=400m/min\times 15$
$=\frac{400}{60}\times 15$
= 100 m
Now, $tan30º=\frac{h}{AC}$
$\therefore h=tan30º\times AC$
$\Rightarrow h=\frac{1}{\sqrt{3}}\times 100$
$=\frac{100}{\sqrt{3}}m$
Correct answer is Option d.