Question

An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will the two planes be after $1\frac{1}{2}$ hours?

• A. $300\sqrt{51}km$
• B. $300\sqrt{61}km$
• C. $350\sqrt{61}km$
• D. $2100km$

Answer 1

The correct option is B

$300\sqrt{61}km$

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
$A{B}^2=A{O}^2+O{B}^2$
$\Rightarrow A{B}^2=(1500{)}^2+(1800{)}^2$
$\Rightarrow AB=\sqrt{2250000+3240000}$
$=\sqrt{5490000}$
$\Rightarrow AB=300\sqrt{61}km$
Hence, the distance between two aeroplanes will be $300\sqrt{61}$ km.