The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds, the angle of elevation becomes 30°. If the aeroplane is flying at a constant height of 3000√3 m, find the speed of the aeroplane.

Let C and E be the initial and final position of the aeroplane

According to the figure,

tan 30° =

⇒

⸫ AD = 3000 × 3 = 9000 m

tan 60° =

⇒

⸫ AB = 3000 m

⸫

Distance travelled in 30 seconds by the aeroplane = BD = 9000 – 3000 = 6000 m

Time given = 30 seconds

Speed = = 200 m/s