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An aircraft execute a horizontal loop at a speed of 720 km h–1, with its wings banked at 15°. The radius of the loop will be [Given: tan15° = 0.268]A 5.71 km B 10.41 km C 15.23 km D 20.63 km

Question

An aircraft execute a horizontal loop at a speed of 720 km h–1, with its wings banked at 15°. The radius of the loop will be [Given: tan15° = 0.268]A 5.71 km B 10.41 km C 15.23 km D 20.63 km

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Solution

To solve this problem, we need to use the formula for the banking of an aircraft, which is:

tan θ = v² / g*r

where: θ is the banking angle, v is the speed of the aircraft, g is the acceleration due to gravity, and r is the radius of the loop.

We are given that tan 15° = 0.268, v = 720 km/h = 200 m/s (since 1 km/h = 5/18 m/s), and g = 9.8 m/s². We need to find r.

Rearranging the formula for r, we get:

r = v² / (g * tan θ)

Substituting the given values, we get:

r = (200 m/s)² / (9.8 m/s² * 0.268)

r = 40000 m²/s² / 2.6244 m/s²

r = 15234.8 m

So, the radius of the loop is approximately 15.23 km, which corresponds to option C.

This problem has been solved

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