A simple flying maneuver

A plane flies horizontally at constant ground speed \(v=720 \textrm{km/h}\). The pilot is informed by an air traffic controller that he must immediately change his direction of flight while keeping the same altitude. The pilot performs a turning maneuver by rolling the plane to a banked position. Then she increases the airspeed in \(\Delta v\) to keep the plane at constant altitude. As a result, the plane describes an arc of radius \(R=8 \textrm {km} \). Find the increase in airspeed \(\Delta v\) in km/h. Assume that the lift force is proportional to the square of the speed and that it is always perpendicular to the plane of the wings.

Details and assumptions

\(g=9.8 m/s^{2}\)

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