A simple flying maneuver

A plane flies horizontally at constant ground speed v=720km/hv=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 Δv\Delta v to keep the plane at constant altitude. As a result, the plane describes an arc of radius R=8kmR=8 \textrm {km} . Find the increase in airspeed Δv\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=9.8m/s2g=9.8 m/s^{2}

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