The angle of elevation of an aeroplane from a point on the ground is $\displaystyle 60$°. After a flight of $\displaystyle 30$ seconds, the angle of elevation from the same point becomes $\displaystyle 30^{\circ}$. If the aeroplane is flying at a constant height of $\displaystyle 3000 \sqrt{3} \mathrm{~m}$, find the speed of the aeroplane.

Let points $\displaystyle A$ and $\displaystyle B$ represent the position of aeroplane. $\displaystyle \tan 60^{\circ}=\frac{3000 \sqrt{3}}{y}=\sqrt{3}$ $\displaystyle \Rightarrow y=3000$ $\displaystyle \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{3000 \sqrt{3}}{x+y}$ $\displaystyle \Rightarrow x=6000$ ∴ Distance $\displaystyle =6000 \mathrm{~m}$, time $\displaystyle =30 \mathrm{sec}$ Speed $\displaystyle =\frac{6000}{30}=200 \mathrm{~m} / \mathrm{s}$.