Question

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

Answer 1

The first aeroplane leaves an airport and flies due north at a speed of $1000$ km per hr.
$\therefore$ Distance travelled in $1.5$ hrs.
$=1000\times 1.5=1500$ km
Similarly, Distance traveled by second aeroplane,
$=1200\times 1.5=1800$ km
In $△ABC$,
$BC$ is distance travelled by first aeroplane and $BA$ is the distance traveled by second aeroplane.
Hence, applying Pythagoras Theorem,
$A{C}^2=A{B}^2+B{C}^2$
$\therefore$ $A{C}^2={1500}^2+{1800}^2$
$\therefore$ $AC=300\sqrt{61}$ km
Hence, two planes are $300\sqrt{61}$ km apart.