Answer:
The radius of curvature of the curved path of the airplane is 23784.356 meters (23.784 kilometers).
Explanation:
We assume that airplane can be represented as a particle. The free body diagram of the vehicle is presented below as attachment, whose variables are:
- Weight of the airplane, measured in newtons.
- Lift, measured in newtons.
- Banking angle, measured in sexagesimal degrees.
The equations of equilibrium associated with the airplane are, respectively:
(Eq. 1)
(Eq. 2)
From (Eq. 2):
In (Eq. 1):
By using the definition of weight, we eliminate the mass of the airplane:
Where:
- Gravitational acceleration, measured in meters per square second.
- Speed, measured in meters per second.
- Radius of curvature, measured in meters.
Lastly, we clear the radius of curvature with the expression:
If we know that ,
and
, the radius of curvature is:
The radius of curvature of the curved path of the airplane is 23784.356 meters (23.784 kilometers).
