Final answer:
The airplane must tilt its wings at an angle where the tangent of that angle equals the aircraft's velocity squared divided by the product of acceleration due to gravity and the turn radius. Physics principles of circular motion are used to calculate the necessary banking angle for achieving the desired turn radius.
Step-by-step explanation:
An airplane generates lift perpendicular to its wings, and when it banks during a turn, a component of this lift provides the centripetal force required for the turn.
To determine how much an airplane should tilt its wings from the horizontal to make a turn with a specific radius at a given speed, one uses principles from physics involving circular motion and the banking of airplanes.
In circular motion, the centripetal force required for an object of mass m moving at speed v along a path with a radius r is given by the equation Fc = mv2/r.
When an airplane banks to make a turn, the lift force can be resolved into two components: a vertical component that balances the plane's weight and a horizontal component that provides the necessary centripetal force.
To find the banking angle θ, we can use the following relation: tan(θ) = v2/(gr), where g is the acceleration due to gravity (approximately 9.81 m/s2). By substituting known values of v and r into this equation, the banking angle θ necessary for the airplane to turn with a given radius can be calculated.