#### Question

An aeroplane leaves an airport and flies due north at a speed of 1000km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1 hours?

#### Solution

Distance traveled by the plane flying towards north in `1 1/2`hrs

`= 1000xx1 1/2=1500`km

Similarly, distance travelled by the plane flying towards west in `1 1/2`hrs

`=1200xx1 1/2=1800`km

Let these distances are represented by OA and OB respectively.

Now applying Pythagoras theorem

Distance between these planes after `1 1/2`hrs AB `=sqrt(OA^2+OB^2)`

`=sqrt(1500^2+1800^2)`

`=sqrt(2250000+3240000)`

`=sqrt5490000`

`=sqrt(9xx610000)`

`=300sqrt61`

So, distance between these planes will be `300sqrt61` km, after `1 1/2`hrs

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#### APPEARS IN

Solution An Aeroplane Leaves an Airport and Flies Due North at a Speed of 1000km/Hr. at the Same Time, Another Aeroplane Leaves the Same Airport and Flies Due West at a Speed of 1200 Km/Hr. How Far Apart Will Be the Two Planes After 1 Hours? Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle.