#### 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/s^{2}

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?

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.