Final answer:
The radius of the circle where an airplane can turn with a centripetal acceleration of 69.6 m/s² and at a speed of 138 m/s is approximately 276 meters.
Step-by-step explanation:
To find the radius of the circle in which an airplane traveling at 138 m/s can turn with a centripetal acceleration of 69.6 m/s², we use the formula for centripetal acceleration, which is a = v²/r, where a is the acceleration, v is the velocity, and r is the radius of the circle.
By rearranging the formula to solve for the radius, we get r = v²/a. Plugging in the given values, the radius r is equal to (138 m/s)² / 69.6 m/s², which equals 138² / 69.6. This results in a radius of approximately 276 m.