An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after 1.5 hours?

The first aeroplane leaves an airport and flies due north at a speed of 1000 km per hr.
∴Distance travelled in 1.5 hrs. = 1000 × 1.5 = 1500 km
Similarly, Distance traveled by second aeroplane = 1200 × 1.5 = 1800 km
In ΔABC, BC is distance travelled by first aeroplane and BA is the distance traveled by second aeroplane.
Hence, applying Pythagoras Theorem, AC² = AB² + BC²
∴AC² = 1500² + 1800²
∴AC = 300√61 km
Hence, two planes are 300√61 km apart.