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 s apart is `30^(@)` , what is the speed of the aircraft ?
A. 10 .8 m `s^(-1)`
B. 1963 m `s^(-1)`
C. 108 m `s^(-1)`
D. 196.3 m `s^(-1)`

Answer 1

Correct Answer - D
O is the observation point at the ground. A and B are the positions of aircraft for which `angleAOB=30^(@)`. Time taken by aircraft from A to B is 10 is.
In `DeltaAOB`,
`tan30^(@)=(AB)/(3400)`
`AB=3400tan30^(@)=(3400)/(sqrt(3))m`
`:.` Speed of aircraft, `v=(AB)/(10)=(3400)/(10sqrt(3))=196.3ms^(-1)`