An aircraft executes a horizontal loop at a ...

Laws of Motion

Question : 30 of 40

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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?

Solution:

Speed of aircraft,

v=720\,\text{km}\,\text{h}^{-1}

=720 \times \frac{5}{18}=200\,\text{m}\,\text{s}^{-1}

angle of banking,

\theta = 15^{\circ}

, radius of the loop

= r = ?

\tan \theta = \frac{v^{2}}{r\,g}

r = \frac{v^{2}}{g \tan \theta}

= \frac{(200)^{2}}{10 \times \tan 15^{\circ}}

= \frac{40000}{10 \times 0.2679}

=14.9 \times 10^{3}\,\text{m}=15\,\text{km}

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