The air is blowing at a speed of 75 knots in the direction of the aircraft flying at a ground speed of 775 knots. The air speed of the aircraft, is
A. 775 knots
B. 75 knots
C. 850 knots
D. 675 knots
The correct answer and explanation is :
The correct answer is C. 850 knots.
Explanation:
To calculate the true airspeed (TAS) of an aircraft, we need to understand the relationship between the ground speed (GS) and wind speed in the context of the aircraft’s motion.
- Ground Speed (GS) is the speed of the aircraft relative to the ground.
- True Airspeed (TAS) is the speed of the aircraft relative to the air mass through which it is flying.
- Wind Speed is the speed of the wind relative to the ground.
The wind can either be in the same direction as the aircraft’s flight path (a tailwind), or opposite to the aircraft’s flight path (a headwind). In this case, the wind is blowing in the direction of the aircraft, which means it’s a tailwind.
The relationship between the ground speed, true airspeed, and wind speed can be expressed as:
[
\text{Ground Speed} = \text{True Airspeed} + \text{Wind Speed}
]
Given:
- Ground Speed (GS) = 775 knots
- Wind Speed = 75 knots (tailwind)
To find the True Airspeed (TAS):
Since the wind is aiding the aircraft, we add the wind speed to the ground speed:
[
\text{True Airspeed (TAS)} = \text{Ground Speed (GS)} + \text{Wind Speed}
]
[
\text{True Airspeed (TAS)} = 775 \text{ knots} + 75 \text{ knots} = 850 \text{ knots}
]
Conclusion:
The true airspeed of the aircraft is 850 knots, which corresponds to option C.