Question

Question 11
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 the two planes be after $1\frac{1}{2}$ hours?

Answer 1

Speed of first aeroplane = 1000 km/hr
Distance covered by first aeroplane due north in
$1\frac{1}{2}hours,\left(OA\right)=1000\times \frac{3}{2}km=1500km$
Speed of second aeroplane = 1200 km/hr
Distance covered by second aeroplane due west in
$1\frac{1}{2}hours,\left(OB\right)=1200\times \frac{3}{2}km=1800km$

In right angle $\Delta AOB$, we have
$A{B}^2=A{O}^2+O{B}^2$ [Using Pythagoras theorem]
$\Rightarrow A{B}^2=(1500{)}^2+(1800{)}^2$
$\Rightarrow AB=\sqrt{2250000+3240000}$
$\Rightarrow$ $AB=\sqrt{5490000}$
$\Rightarrow AB=300\sqrt{61}km$
Hence, the distance between two aeroplanes will be $300\sqrt{61}km$.