Question

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 \(1\frac{1}{2}\) hours?

Answer 1

Distance travelled by aeroplane towards North is  1\(\frac{1}{2}\)hours :

= 1000 x 1\(\frac{1}{2}\)

= 1000 x \(\frac{3}{2}\)

= 1500 km. 

Distance travelled by aeroplane towards West in  1\(\frac{1}{2}\)Hours :

= 1200 x  1\(\frac{1}{2}\)

= 1200 x \(\frac{3}{2}\)

= 1800 km. 

In ⊥∆AOB, 

AB² = OA² + OB² 

= (1500)² + (1800)² 

= 2250000 + 3240000 = 5490000

∴ Two planes are 300V 6T km. apart after 14 hours