The angle of elevation of an aeroplane from P on the ground is 60°. After a flight of 20 seconds horizontally, the angle of elevation changes 30°. Find the constant height at which the aeroplane is flying, if the aeroplane is flying at a speed of 300 m/s?

Question

The angle of elevation of an aeroplane from P on the ground is 60°. After a flight of 20 seconds horizontally, the angle of elevation changes 30°. Find the constant height at which the aeroplane is flying, if the aeroplane is flying at a speed of 300 m/s?

3000(√3 - 1) m
1500(√3 + 1) m
3000√3 m
6000√3 m

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AhmedNazir · Answer 1 · Sep 04, 2022 04:29:57

Option 3 : 3000√3 m

Given:

Speed of the aeroplane = 300 m/s

Time = 20 sec

Formula Used:

Distance = Time × Speed

Calculation:

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Suppose A be the point of observation.

Also, E and D be positions of the aeroplane initially and after 20 sec, respectively.

BE = CD = Constant height

∠CAE = 60° and ∠CAD = 30°

Suppose, BE = CD = h meter

AB = x meters

The distance covered in 20 seconds, BC = ED = 20 × 300 = 6000 m

So, AC = (x + 6000) m

In ΔACD, ∠ACD = 90° and ∠CAD = 30°

⇒ tan30° = CD/AC

⇒ 1/√3 = h/(x + 6000)

⇒ h = (x + 6000)/√3 ------- (i)

In ΔBAE, ∠ABE = 90° and ∠BAE = 60°

⇒tan60° = BE/AB

⇒ ∠3 = h/x

⇒ h = √3x ------ (ii)

From (i) and (ii), we have –

⇒ √3 x = (x + 6000)/√ 3

⇒ 3x = x + 6000

⇒ 2x = 6000

⇒ x = 3000 m

Thus, from (ii), h = x√3 = 3000√3 m

∴ The constant height at which the aeroplane is flying is 3000√3 m.

The angle of elevation of an aeroplane from P on the ground is 60°. After a flight of 20 seconds horizontally, the angle of elevation changes 30°. Find the constant height at which the aeroplane is flying, if the aeroplane is flying at a speed of 300 m/s?

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