Question

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 $g=10\, m s^{-2}, tan \,15^{\circ}=0.27$)

• A. $14.8 \, km$
• B. $14.8\, m$
• C. $29.6\,km$
• D. $29.6\, m$

Answer 1

Answer: (A)

$14.8 \, km$

Answer 2

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