An aircraft executes a horizontal loop at a speed
Question.
An aircraft executes a horizontal loop at a speed of $720 \mathrm{~km} / \mathrm{h}$ with its wings banked at $15^{\circ}$. What is the radius of the loop?

solution:

Speed of the aircraft, $v=720 \mathrm{~km} / \mathrm{h}=720 \times \frac{5}{18}=200 \mathrm{~m} / \mathrm{s}$

Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^{2}$

Angle of banking, $\theta=15^{\circ}$

For radius $r$, of the loop, we have the relation:

$\tan \theta=\frac{v^{2}}{r g}$

$r=\frac{v^{2}}{g \tan \theta}$

$=\frac{200 \times 200}{10 \times \tan 15}=\frac{4000}{0.268}$

$=14925.37 \mathrm{~m}$

$=14.92 \mathrm{~km}$
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