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An aircraft is flying at a height of 340...

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)`

Text Solution

Verified by Experts

The correct Answer is:
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)`
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