An aircraft is flying at a steady altitude of 1000 meters. From a point on the ground, the angle of elevation of the airplane changes from 60° to 45° in 20 seconds as it flies directly away from the observer. What is the approximate speed of the airplane?
Show answer & explanation
Correct answer: B
Explanation
Height of the airplane = 1000 meters
First position –
tan 60° = 1000 / x
x = 1000/√3 meters
Second position –
tan 45° = 1000 / y
y = 1000 meters
Distance covered by the airplane in 20 seconds:
= y − x
= 1000 − 1000/√3
≈ 1000 − 577.35
≈ 422.65 meters
Speed = 422.65 ÷ 20
≈ 21.1 meters/second