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An aeroplane is circling above an airport in a horizontal circle at a speed of 400 kmh-1.The banking angle of the wings is 20.What is the radius of the circular path?

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Answer: the radius of the circular path is approximately 1637.58 meters.

Step-by-step explanation:

The centripetal force acting on the airplane is provided by the component of the gravitational force that acts towards the center of the circular path. This component is given by:

F_c = m * g * tan(banking angle)

Where:

F_c is the centripetal force

m is the mass of the airplane

g is the acceleration due to gravity

tan(banking angle) is the tangent of the banking angle

Now, the centripetal force is also given by the formula:

F_c = (m * v^2) / r

Where:

v is the speed of the airplane

r is the radius of the circular path

Equating the two expressions for F_c, we get:

(m * g * tan(banking angle)) = (m * v^2) / r

Canceling out the mass (m) on both sides of the equation, we have:

g * tan(banking angle) = v^2 / r

Solving for r, we get:

r = (v^2) / (g * tan(banking angle))

Substituting the given values:

v = 400 km/h = 400,000 m/h

g = 9.8 m/s^2

banking angle = 20°

Converting the speed to m/s:

v = 400,000 m/h * (1/3600) h/s = 111.11 m/s

Converting the banking angle to radians:

banking angle = 20° * (π/180) rad/° = 0.3491 rad

Now, substituting the values into the formula:

r = (111.11^2) / (9.8 * tan(0.3491))

r ≈ 1637.58 meters

Therefore, the radius of the circular path is approximately 1637.58 meters.

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