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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? - ISC (Commerce) Class 11 - Physics (Theory)

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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?

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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Solution 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? Concept: Newton’s Second Law of Motion.
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