An aircraft executes a horizontal loop at a speed of 720 km h^-1 with its wings banked at $15°$. What is the radius of the loop? 

(Take $g=10 m s^{-2}, \tan 15°=0.27$)

 

Here, 

            $$\begin{gathered} v=720 km h^{-1} \\ =720\times \frac{5}{18} m s^{-1} \\ =200 m s^{-1} \\ \theta =15° , g=10 m s^{-2}; \\ As \tan \theta =\frac{v^2}{rg} \\ \therefore r=\frac{v^2}{\tan \theta g} \\ =\frac{{(200 m s^{-1})}^2}{\tan 15°\times 10 m s^{-2}} \\ =14815 m \\ =14.8 km \end{gathered}$$