# Find the gliding distance of an aircraft.

Find the gliding distance of an aircraft flying at an altitude of \(1500\,m\) with a maximum lift to drag ratio of \(8\).

Aircraft starts to glide at an altitude of \(1500\,m\).

From the figure,

\[\tan \theta = \frac{h}{D} \Rightarrow D = \frac{h}{{\tan \theta }}\]

For the unaccelerated glide, in equilibrium \(L = W\cos \theta \), \(D = W\sin \theta \),

\[ \Rightarrow \left( {\frac{L}{D}} \right) = \frac{{W\cos \theta }}{{W\sin \theta }} = \left( {\frac{1}{{\tan \theta }}} \right)\]

On putting the values , to calculate the distance

\[D = \frac{h}{{\tan \theta }} = h\left( {\frac{L}{D}} \right) = 1500 \times 8 = 12000\,m\]