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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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ConceptNewton’s Second Law of Motion

#### 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

Is there an error in this question or solution?

#### APPEARS IN

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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