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?
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:
$\tan \theta=\frac{v^{2}}{r g}$
$r=\frac{v^{2}}{g \tan \theta}$
$=\frac{200 \times 200}{10 \times \tan 15}=\frac{4000}{0.268}$
$=14925.37 \mathrm{~m}$
$=14.92 \mathrm{~km}$
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:
$\tan \theta=\frac{v^{2}}{r g}$
$r=\frac{v^{2}}{g \tan \theta}$
$=\frac{200 \times 200}{10 \times \tan 15}=\frac{4000}{0.268}$
$=14925.37 \mathrm{~m}$
$=14.92 \mathrm{~km}$