question_answer

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 10s apart is 30°, then the speed of the aircraft is

A)  \[19.63\,m{{s}^{-1}}\]        

B)                         \[1963\,m{{s}^{-1}}\]      

C)             \[108\,m{{s}^{-1}}\]      

D)         \[196.3\,m{{s}^{-1}}\]

E)  \[10.8\,m{{s}^{-1}}\]

Correct Answer: D

Solution :

\[\tan \theta =\frac{L}{A}\] \[\tan {{30}^{o}}=\frac{10v}{3400}\] \[v=\frac{340}{\sqrt{3}}=196.3\,m{{s}^{-1}}\]