Motion in a plane NCERT Solutions Class 11 Physics - Solved Exercise Question 4.25

Question 4.25:

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 ?

Solution:

The positions of the observer and the aircraft are shown in the given figure.
Height of the aircraft from ground, OR = 3400 m
Angle subtended between the positions, ∠POQ = 30°
Time = 10 s
In ΔPRO:
tan 150 = PR / OR
PR = OR tan 150
= 3400 X tan 150

ΔPRO is similar to ΔRQO.
∴PR = RQ
PQ = PR + RQ
= 2PR = 2 × 3400 tan 15°
= 6800 × 0.268 = 1822.4 m

∴ Speed of the aircraft = 1822.4 / 10 = 182.24 m/s

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