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The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?

The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane? Correct Answer 100√3

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From the figure,

tan 60° = 4500/x

⇒ x = 4500/√3

 And tan 30° = 4500/(x + y)

⇒ x + y = 4500√3

⇒ y = 4500√3 - 4500/√3

⇒ y = (13500 - 4500)/√3 = 9000/√3 = 3000√3

∴ Speed = 3000√3/30 = 100√3 mtr/sec

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