Question

An aircraft executes a horizontal loop of radius 9 km at a constant speed of 540 km/h. The wings of the aircraft are banked at an angle of

• A. \( \sec^{-1}(4) \)
• B. \( \cot^{-1}(4) \)
• C. \( \tan^{-1}(4) \)
• D. \( \sec^{-1}(4) \) \bigskip

Hint:

At half the maximum height, the vertical velocity decreases due to gravity, but the horizontal velocity remains unchanged. Using kinematic equations and velocity components, the total speed can be determined.

Answer 1

The Correct Option is B

For an aircraft executing a horizontal loop, the bank angle \( \theta \) is given by: \[ \tan \theta = \frac{v^2}{g r}, \] where \( v \) is the velocity, \( g \) is the acceleration due to gravity, and \( r \) is the radius of the loop. Substituting the given values of velocity \( v = 540 \) km/h, radius \( r = 9 \) km, and \( g = 10 \, \text{m/s}^2 \), we can find \( \theta \), which is \( \cot^{-1}(4) \).