Ncert Exercises & Solutions

5.30 An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?

G i v e n,

S p e e d o f a i r c r a f t, v = 720 k m h^{- 1} = 720 \times \frac{5}{18} = 200 m s^{- 1}

A n g l e o f b a n k i n g, θ = 15^{0}

\tan θ = \frac{v^{2}}{r g}

\Rightarrow r = \frac{v^{2}}{g \times \tan θ} = \frac{{(200)}^{2}}{10 \times \tan 15^{0}}

\Rightarrow r = \frac{40000}{10 \times 0.2679} = 14.9 \times 10^{3} m

\Rightarrow r = 15 k m