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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:
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Verified Answer
Given,
$$
\begin{aligned}
&\alpha=15^{\circ}, v=720 \mathrm{~km} / \mathrm{h}=200 \mathrm{~m} / \mathrm{s}, g=10 \mathrm{~ms}^{-2} . \\
&\therefore \tan \alpha=v^2 / r g, \\
&r=v^2 / g \tan \alpha=(200)^2 /\left(10 \times \tan 15^{\circ}\right)=15.23 \mathrm{~m}
\end{aligned}
$$
$$
\begin{aligned}
&\alpha=15^{\circ}, v=720 \mathrm{~km} / \mathrm{h}=200 \mathrm{~m} / \mathrm{s}, g=10 \mathrm{~ms}^{-2} . \\
&\therefore \tan \alpha=v^2 / r g, \\
&r=v^2 / g \tan \alpha=(200)^2 /\left(10 \times \tan 15^{\circ}\right)=15.23 \mathrm{~m}
\end{aligned}
$$
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