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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 be the two planes after 1 1/2 hours?

Q11  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 be the two planes after 1 1/2  hours?

Answers (1)
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Distance travelled by the first aeroplane due north in $1\frac{1}{2}$ hours.

$=1000\times \frac{3}{2}=1500 km$

Distance travelled by second aeroplane due west in $1\frac{1}{2}$ hours.

$=1200\times \frac{3}{2}=1800 km$

OA and OB are the distance travelled.

By Pythagoras theorem,

$AB^2=OA^2+OB^2$

$\Rightarrow AB^2=1500^2+1800^2$

$\Rightarrow AB^2=2250000+3240000$

$\Rightarrow AB^2=5490000$

$\Rightarrow AB^2=300\sqrt{61}km$

Thus, the distance between the two planes is $300\sqrt{61}km$.

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