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The angle of elevation of an airplane from a point A on the ground is $60 °$ , After a flight of 30 seconds, the angle of elevation changes to $30 °$ . If the plane is flying at a constant height of $36003 m$ , find the speed in $km / hr$ of the plane.

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864 km/hr

866 km/hr

865 km/hr

870 km/hr

answer is B.

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Detailed Solution

Given that the angle of elevation of an airplane from a point A on the ground is

60 °

. After a flight of 30 seconds. The angle of elevation changes to

30 °

. We have to find the speed of the plane if the airplane is flying at a constant height of

36003 m

In a right-angle triangle, tan θ = Opposite side Hypotenuse

Let us suppose that AB = x and AC = y.
The angle of elevation of a jet plane from a point A on the ground is 60^â . After a flight of 15 second, the angle of elevation changes to 30^â .

The angle of elevation of a jet plane from a point A on the ground is 60^â . After a flight of 15 second, the angle of elevation changes to 30^â .

In right

Δ A B P

, we have

tan 60 ° = P B A B ⇒ 3 = 36003 x ⇒ x = 3600

tan 30 ° = QC AC ⇒ 13 = 36003 A C ⇒ A C=10800 ⇒ A C+AB=10800 ⇒ y + x = 10800 ⇒ y + 3600 = 10800 ⇒ y = 10800 - 3600 ⇒ y = 7200 ∴ AB = AC = 7200

We know that,

Speed = Distance Time ⇒ Speed = 720030 ⇒ Speed=240 m/s ⇒ Speed=240× 185 ⇒ Speed=864 km/hr

Hence, the speed of the airplane is

864 km / hr

.
Therefore, the correct option is 2.

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