-
An aeroplane flying horizontally at a height of 3 km. above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 seconds of flight, its angle of elevation is changed to 30°. The speed of the aeroplane (Take, √3 = 1.732) is
-
- 230.63 m./sec.
- 230.93 m./sec.
- 235.85 m./sec.
- 236.25 m./sec.
Correct Option: B
AB = CD = 3000 metre
A and C = Positions of aeroplane
∠AOB = 60°; ∠COD = 30°
In ∆OAB,
| tan 60° = | OB |
| ⇒√3 = | OB |
| ⇒ OB = | √3 |
= 1000 √3 metre
In ∆OCD,
| tan 30° = | OD |
| ⇒ | = | √3 | OD |
⇒ OD = 3000 √3 metre
∴ BD = (3000 √3 – 1000 √3 ) metre
= 2000 √3 metre
∴ Speed of aeroplane
| = | m./sec. | 15 |
| = |  | 2000 × 1.732 |  | m./sec. | ||
| 15 |
= 230.93 m./sec.
