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The angle of elevation of an airplane from a point A on the ground is $60 °$ , After a flight of 15 seconds, the angle of elevation changes $30 °$ . If the airplane is flying at a constant height of $15003 m$ , find the speed of the plane in km/hr.

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630 km/hr

700 km/hr

720 km/hr

840 km/hr

answer is C.

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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 5seconds The angle of elevation changes to

30 °

. We have to find the speed of the plane in km/hr, if the airplane is flying at a constant height of 1500m.

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

Height of airplane

= BD = CE = 15003 m

and

∠ BAE = 60 ° a n d ∠ CAE = 30 °

In triangle ADB,

tan 60 ° = 15003 AD ⇒ 3 = 15003 AD ⇒ AD = 1500 m

In triangle CAE,

tan 30 ° = 15003 AE ⇒ 13 = 15003 AD ⇒ AE = 1500 × 3 = 4500 m

Distance covered by plane in 15 seconds:

BC = DE ⇒ BC = AE − AD ⇒ BC = 4500 - 1500 ⇒ BC= 3000 m

Speed of airplane:

⇒ Speed= 300015 ⇒ Speed=200 m/s ⇒ Speed=720 km/hr

The speed of the airplane is

720 km / hr

.
Therefore, the correct option is 3.

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