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?

• A. $300\sqrt{5}m$
• B. $300m$
• C. $300\sqrt{61}m$
• D. $3000m$

Answer 1

Answer: (C)

$300\sqrt{61}m$

The first plane travels distance $BC$ in the direction of north in $1\frac{1}{2}$ hours at a speed of $1000km/hr$.
$\therefore$ $BC=1000\times \frac{3}{2}km=1500km$
The second plane travels distance $BA$ in the direction of west in $1\frac{1}{2}$ hours at a speed of $1200km/hr$.
$\therefore$ $BA=1200\times \frac{3}{2}km=1800km$
From right angles $△ABC$,
${AC}^2={AB}^2+{BC}^2$
$={\left(1800\right)}^2+{\left(1500\right)}^2$
$=3240000+2250000=5490000$
$\Rightarrow$ $AC=\sqrt{5490000}m$
$\Rightarrow$ $AC=300\sqrt{61}m$