Question

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 a part is 30°, what is the speed of the aircraft?

Answer 1

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 15^@  =(PR)/(OR)`

`"PR" = "OR"  tan 15^@`

`=3400 xx tan 15^@`

`= 3400 xx 0.2679 = 910.86`

ΔPRO is similar to ΔRQO.

∴PR = RQ

PQ = PR + RQ

= 2PR

= 2 × 910.86 = 1821.72 m

∴ Speed of aircraft = `1821.72/10 = 182.2 "m/s"`