An aircraft records a ground speed of 775 knots with a tailwind of 75 knots (wind blowing in the same direction as the aircraft). What is the true air speed of the aircraft?

Introduction:This problem checks the relationship between air speed, ground speed, and wind. Ground speed reflects the aircraft’s motion over the ground, while air speed reflects motion relative to the surrounding air mass. Wind adds or subtracts from air speed to yield ground speed.

Given Data / Assumptions:

• Ground speed (GS) = 775 knots.
• Wind speed (tailwind) = 75 knots, acting in the same direction as flight.
• Air speed (TAS, simplified here) is required.

Concept / Approach:

For collinear wind, GS = TAS + tailwind and GS = TAS − headwind. With a tailwind, subtract the wind from ground speed to get air speed.

Step-by-Step Solution:

Verification / Alternative check:

If the wind were a headwind of 75 knots, TAS would be GS + 75 = 850 knots, which does not match the stated tailwind condition.

Why Other Options Are Wrong:

• 775 knots: That is the ground speed, not the air speed.
• 75 knots: That is only the wind speed.
• 850 knots: Would correspond to a 75-knot headwind, not a tailwind.
• 675 knots: No combination here gives 675 with a 75-knot tailwind and 775 ground speed.

Common Pitfalls:

• Adding the wind to ground speed under tailwind conditions instead of subtracting.
• Confusing indicated air speed with true air speed; here we treat air speed generically as speed relative to air.

Final Answer:

700 knots