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 apart is 30°, what is the speed of the aircraft ?
Given: The height at which aircraft is flying is 3400 m , the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30 ° .
The situation is shown in figure below.
OC is the height of the aircraft. In 10 s the aircraft covers a distance AB.
In triangle AOC,
tan θ = AC OC AC = OC × tan θ
By substituting the given values in the above expression, we get
AC = 3400 × tan ( 15 ° ) = 911 m
The distance covered by aircraft in 10 s is,
AB = 2 AC = 2 × 911 = 1822 m
The speed of the aircraft is given as,
v = distance time = AB t
By substituting the given values in the above expression, we get
v = 1822 10 = 182.2 ms − 1
Thus, the speed of the aircraft is 182.2 ms − 1 .
Given: The height at which aircraft is flying is
The situation is shown in figure below.
OC is the height of the aircraft. In
In triangle AOC,
By substituting the given values in the above expression, we get
The distance covered by aircraft in
The speed of the aircraft is given as,
By substituting the given values in the above expression, we get
Thus, the speed of the aircraft is
