An aeroplane flies level at a height of 2400 m. From a point O on the ground its angle of elevation is 60°, and 10 seconds later it is 45°. Find its speed.

Horizontal distances: 2400 cot 60° = 800√3 m and 2400 cot 45° = 2400 m. Distance flown = 2400 − 800√3 = 800(3 − √3) m in 10 s, i.e. 80(3 − √3) m/s = 80(3 − √3) × 18/5 = 288(3 − √3) km/h (about 365 km/h).