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Question
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?
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Solution 1
Here v = 720 km/h = `720xx 5/18` m/s = 200 m/s and angle of banking `theta = 15^@`
From the relation
`tan theta = v^2/"rg"` we have
`r = v^2/(g tan theta) = (200xx200) /(10 xx tan 15^@) = (200xx200)/(10xx0.2679)`
=> r = 14931 m = 14.9 km
Solution 2
Speed of the aircraft, v = 720 km/h = `720xx5/18 = 200` m/s
Acceleration due to gravity, g = 10 m/s2
Angle of banking, θ = 15°
For radius r, of the loop, we have the relation:
`tan theta = v^2/"rg"`
`r = v^2/(g tan theta)`
`= (200xx200)/(10xx tan 15) = 4000/0.268`
= 14925.37 m
= 14.92 km
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