Question

A plane is flying horizontally at a height of $1\text{km}$ from ground. Angle of elevation of the plane at a certain instant is $60°.$ After $20$ seconds angle of elevation is found $30°.$ The speed of plane is

• A. $\frac{100}{\sqrt{3}}\text{m/s}$
• B. $\frac{200}{\sqrt{3}}\text{m/s}$
• C. $100\sqrt{3}\text{m/s}$
• D. $200\sqrt{3}\text{m/s}$

Answer 1

The correct option is A $\frac{100}{\sqrt{3}}\text{m/s}$


$\tan 60°=\frac{QN}{LN}\Rightarrow LN=\frac{1000}{\sqrt{3}}m$
Similarly,
$LM=1000\sqrt{3}m$

Hence the speed of the plane,
$=\frac{LN-LM}{20}m/s=\frac{2000}{20\sqrt{3}}m/s=\frac{100}{\sqrt{3}}m/s$