Question

An aeroplane leaves an airport and flies due north at a speed of 1000 km/hr. At the time, another aeroplane leaves the same airport and flies due west at a speed 1200 km/hr. How far apart will be the two planes after $1\frac{1}{2}$ hours ?

Answer 1

Let the start point of both aeroplanes be $B$

The final position of aeroplane 1 be $A$

The final position of aeroplane 2 be $C$

$speed=\frac{distance}{time}$

$AB=1000\times \frac{3}{2}$

$AB=1500km$

$BC=1200\times \frac{3}{2}$

$BC=1800km$

Applying Pythagoras theorem

$A{C}^2=A{B}^2+B{C}^2$

$A{C}^2=(1500{)}^2+(1800{)}^2$

$AC=\sqrt{5490000}=2343.07km\approx 2343km$

The distance between two aeroplanes is $\approx 2343km$