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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
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- 600
- 600 (√3 + 1)
- 600 √3
- 600 (√3 - 1)
Correct Option: D
Let A and C be the positions of plane.
AB = CD = 2500 metre
BD = AC = x metre (let)
∠AOB = 60° ; ∠COD = 30°
In ∆OAB,
⇒ OB = 2500 metre
In ∆OCD,
| tan30° = | OD |
| ⇒ | √3 |
| = | 2500 + x |
⇒ 2500 + x = 2500√3
⇒ x
= 2500 √3 – 2500
= 2500 (√3 - 1) metre
Time = 15 seconds
| = | hour = | hour | 60 × 60 | 240 |
| ∴ Speed of plane = | × 240 kmph | 1000 |
= 600 (√3 - 1) kmph.
