An airplane is flying with constant speed of 300 m/s along a horizontal circle with a radius of 15,000 m. If the lift force of the air on the wings is perpendicular to the wings, at what angle relative to the horizontal should the wings be banked?
A) 15.1°
B) 22.2°
C) 31.5°
D) 37.7°
E) 63.0°

Question

Quizplus · Accepted Answer

In order to keep a circular motion, the lift force must provide the necessary centripetal force. This can be achieved by banking the wings at an angle relative to the horizontal plane. The angle of bank can be determined using the equation:

tan(θ) = (v^2) / (r g)

where θ is the angle of bank, v is the speed of the airplane, r is the radius of the circular path, and g is the acceleration due to gravity.

Substituting the given values, we get:

tan(θ) = (300^2) / (15,000 × 9.81)
θ ≈ 31.5°

Therefore, the wings should be banked at an angle of approximately 31.5° relative to the horizontal plane. The correct answer is C.

An Airplane Is Flying with Constant Speed of 300 M/s