An aircraft executes a horizontal loop at a speed of $720\; km/h$ with its wings banked at $15^o$. What is the radius of the loop in $km$?
An aircraft executes a horizontal loop at a speed of $720\; km/h$ with its wings banked at $15^o$. What is the radius of the loop in $km$?
Speed of the aircraft, $v=720 \,km / h =720 \times \frac{5}{18}=200 \,m / s$
Acceleration due to gravity, $g$ $=10 \,m / s ^{2}$
Angle of banking, $\theta=15^{\circ}$
For radius $r,$ of the loop, we have the relation:
$\tan \theta=\frac{v^{2}}{r g}$
$r=\frac{v^{2}}{g \tan \theta}$
$=\frac{200 \times 200}{10 \times \tan 15}=\frac{4000}{0.268}$
$=14925.37\, m$
$=14.92\, km$
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