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)

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 $15 °$ = 0.27)

Smart Achievers · Accepted Answer

(1)

Here, $v = 720 {km h}^{- 1} = 720 \times \frac{5}{18} {m s}^{- 1} = 200 {m s}^{- 1}$

$θ = 15 °, g = 10 {m s}^{- 2}; As \tan θ = \frac{v^{2}}{r g}$

$∴$ $r = \frac{v^{2}}{\tan θ g} = \frac{{(200 {m s}^{- 1})}^{2}}{\tan 15 ° \times 10 {m s}^{- 2}} = 14815 m = 14.8 km$

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