Question

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? (hint: the vertical component of wing-lift supports the plabes weight, and the horizontal component is the force that results in a centripetal acceleration.)

Answer 1

The banking angle of the wings should be approximately 89.4 degrees relative to the horizontal.

Step-by-step explanation:

When an airplane is flying in a horizontal circle, the lift force of the air on the wings needs to be angled in order to provide the necessary centripetal acceleration. This angle is known as the banking angle. In this case, the airplane is flying with a constant speed of 300 m/s and the radius of the circle is 15,000 m.

To find the angle, we can consider the vertical and horizontal components of the lift force. The vertical component balances the weight of the airplane, while the horizontal component provides the necessary centripetal acceleration. The tangent of the banking angle can be found by dividing the vertical component of lift by the horizontal component.

Tan(θ) = (mg)/(mv²/r)

= (mvr)/(mv²)

= r/v

Therefore, the tangent of the banking angle is equal to the ratio of the radius to the speed of the airplane. Substituting the given values, we have:

Tan(θ) = 15000/300

= 50.

Taking the inverse tangent of 50, we find that the banking angle, θ, is approximately 89.4 degrees relative to the horizontal.