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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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