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The angle of elevation of an aeroplane from a point on the ground is 45°. After flying for 15 seconds, the elevation changes to 30°. If the aeroplane is flying at a height of 2500 metres, then the speed of the aeroplane in km/ hr. is

A) \( \Large 600 \)
B) \( \Large 600(\sqrt{3}+1) \)
C) \( \Large 600\sqrt{3} \)
D) \( \Large 600(\sqrt{3}-1) \)

Correct Answer:




D) \( \Large 600(\sqrt{3}-1) \)

Description for Correct answer:

\(\Large In\ \triangle ABE, \)

\( \Large tan45=\frac{2500}{AB} \)

\( \Large AB=2500 \)

\( \Large In\triangle ACD, \)

\( \Large tan30=\frac{2500}{AC} \)

\( \Large AC=2500\sqrt{3} \)

Distance covered by Aeroplane in 15 sec.

\( \Large =AC-AB=2500\sqrt{3}-2500 \)

\( \Large =2500(\sqrt{3}-1) \)

\( \Large speed=\frac{2500(\sqrt{3}-1)}{15}m/s \)

\( \Large =\frac{2500(\sqrt{3}-1)}{15} \times \frac{18}{5}km/hr. \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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Similar Questions

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