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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 1200 km per hour. How far apart will be the two planes after` 1 1/2` hours?
Solution
Let A be the first aeroplane flied due north at a speed of 1000 km/hr and B be the second aeroplane flied due west at a speed of 1200 km/hr
Distance covered by plane A in` 1 1/2 hours=1000xx3/2=1500km`
Distance covered by plane B in `1 1/2 hours = 1200xx3/2=1800 km`
Now, In right triangle ABC
By using Pythagoras theorem, we have
`AB^2=BC^2+CA^2`
=(1800)^2+(1500)^2
=3240000+2250000
=5490000
∴ `AB^2=5490000 `
⇒` AB=300sqrt61m`
Hence, the distance between two planes after `1 1/2 house is 300 sqrt61m`
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