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Q. An aircraft executes a horizontal loop at a speed of $800 km / h$ with the wings banked at an angle of $30^{\circ} .$ What is the radius of the loop?

Laws of Motion

Solution:

$v =800 \times \frac{5}{18}=222.2 m / s$
As we know that
$\tan \theta=\frac{v^{2}}{r g}$
$ \Rightarrow r=\frac{v^{2}}{g \tan \theta}$
$r=\frac{222.2 \times 222.2}{\frac{1}{\sqrt{3}} \times 9.8}$
$=\frac{49372.84}{9.8} \times 1.71$
$r=5038 \times 1.71=8615.05$
$=8.615 \times 10^{3} m$