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° then the speed of the aircraft is

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° then the speed of the aircraft is (A)  19.63 ms-1  (B)  196.3 ms-1  (C)  108 ms-1  (D)  1963 ms-1

Tardigrade Admin · Accepted Answer

O is the observation point at the ground. A and B are the positions of aircraft for which angle AOB=30Â°. Time taken by aircraft from A to B is 10 s. In Δ AOB, tan 30° =(AB/3400) AB=3400 tan 30° =(3400/√3)m ∴ Speed of aircraft, v=(AB/10) =(3400/10√3) =196.3 ms-1

Q. 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 $3 0^{\circ}$ then the speed of the aircraft is

$19.63 m s^{- 1}$

$196.3 m s^{- 1}$

$108 m s^{- 1}$

$1963 m s^{- 1}$

$10.8 m s^{- 1}$

Q. An aircraft is flying at a height of 3400m 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

19.63ms−1

196.3ms−1

108ms−1

1963ms−1

10.8ms−1