Given:
Radius of the circular path is
[tex]r=2200\text{ m}[/tex]
The speed of the airplane is
[tex]v=400\text{ km/h}[/tex]
Required:
calculate the banking angle
Explanation:
we will use the formula to calculate the banking that is given as
[tex]\tan\theta=\frac{v^2}{rg}[/tex]
here r is the radius and v is velocity of the plane
first, convert velocity in m/s
[tex]\begin{gathered} v=\frac{400\text{ km}}{\text{ h}} \\ v=\frac{400\text{ km}}{\text{ h}}\times\frac{1000\text{ m}}{\text{ km}}\times\frac{1\text{ h}}{3600\text{ s}} \\ v=111.11\text{ m/s} \end{gathered}[/tex]
plugging all the values in the above formula, we get
[tex]\begin{gathered} \tan\theta=\frac{(111.11\text{ m/s})^2}{2200\text{ m}\times9.8\text{ m/s}^2} \\ \tan\theta=\frac{12345.4321}{21560} \\ \tan\theta=0.5726 \\ \theta=\tan^{-1}(0.5726) \\ \theta=29.79^{\degree} \end{gathered}[/tex]
Thus, the angle is
[tex]29.79^{\degree}[/tex]
