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  4. An aircraft executes a horizontal loop at a speed of 720 km h-1 with its wings banked at 15°. What is the radius of the loop? (Take g=10 m s-2, tan 15°=0.27)

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Q. An aircraft executes a horizontal loop at a speed of $720\, km$ $h^{-1}$ with its wings banked at $15^°$. What is the radius of the loop? (Take $g=10\, m s^{-2}, tan \,15^{\circ}=0.27$)

Laws of Motion

Solution:

Here, $v=720 \,km$ $h^{-1}$ $=720\times\frac{5}{18}m$ $s^{-1}$ $=200\, m$ $s^{-1}$
$\theta=15^{\circ}$, $g=10 \,m s^{-2}$ As tan $\theta=\frac{v^{2}}{rg}$
$\therefore \quad$ $ r=\frac{v^{2}}{tan\,\theta\, g}$ $=\frac{\left(200\, m\, s^{-1}\right)^{2}}{tan\, 15^{\circ}\times10 \,m \,s^{-2}}$ $=14815 \,m=14.8 \,km$