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Home » An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft?
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft?
CBSE | Class 11 | Motion in a Plane | NCERT | Physics
An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft?

Answer :

According to the question, the aircraft is flying at a height = 3400 m

Let A and B represent the positions of aircraft which make an angle ∠AOB = 300. OC is a perpendicular drawn on AB. OC represents the height of the aircraft. It is equal to 3400 m and

∠AOC =  ∠COB = 150.

In ΔAOC,

AC = OC tan 150

AC = 3400 x 0.267

AC = 910.86 m

Now, AB = AC + CB

AB = AC + AC = 2 AC

AB = 2 x 910.86 m

We can determine the speed of the aircraft in the following manner

Speed = distance AB/time

= (2 x 910.86)/10= 182.17 m/s

Speed = 182.2 m/s

 

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