An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time,

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Question 11 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 of1200 km per hour. How far apart will be the two planes after $1\dfrac{1}{2}$ hours?

Solution:

Given

Speed of first aeroplane = 1000 km/hr

Distance covered by first aeroplane flying due north in

$1\dfrac{1}{2}$ hours (OA) = 1000 × $\dfrac{3}{2}$ km = 1500 km

Speed of second aeroplane = 1200 km/hr

Distance covered by second aeroplane flying due west in

$1\dfrac{1}{2}$ hours (OB) = 1200 × $\dfrac{3}{2}$ km = 1800 km

In right angle ΔAOB, by Pythagoras Theorem,

AB^2 = AO^2 + OB^2

AB2 = $(1500)^2 + (1800)^2$

AB = $\sqrt{(2250000 + 3240000)}$

= $\sqrt{5490000}$

AB = 300$\sqrt{61}$ km

Hence, the distance between two aeroplanes will be 300 $\sqrt{61}$ km.

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