A plane flies above a man at a height of 1000 m. At one time, angle of elevation is 60°. Suddenly, the plane climbs up at an angle of 30° and 5 seconds later angle of elevation becomes 45°. Speed of plane is?
Explanation:
Given, height of plane initially (BC) = 1000 meters.
Let CF = x
In ∆CFE, cos30° = √3/2 = CE/CF
⇒ CE = √3x/2 = BD …(1)
Also, sin30° = 1/2 = FE/CF
⇒ FE = x/2 …(2)
In ∆ABC, tan60° = √3 = CB/AB
⇒ AB = CB/√3 = 1000/√3 …(3)
In ∆AFD, tan45° = 1 = FD/AD
⇒ AD = FD …(4)
We know, BD = AD – AB = FD – AB
⇒ BD = (DE + EF) - AB
From (1), (2) and (3)
√3x/2 = (1000 + x/2) – 1000/√3
Solving this we get x = 2000/√3
∴ Plane travels 2000/√3 meters in 5 seconds.
⇒ Speed of the plane = (2000/√3) ÷ 5 = 400/√3.
Hence, option (d).
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