Question

If the lift of the airplanes wings are perpendicular to the wings at what angles to the plane be banked so that it doesn’t tend to slip sideways

Answer 1

Given:

Radius of the circular path is

`r=2200\text{ m}`

The speed of the airplane is

`v=400\text{ km/h}`

Required:

calculate the banking angle

Step-by-step explanation:

we will use the formula to calculate the banking that is given as

`\tan\theta=(v^2)/(rg)`

here r is the radius and v is velocity of the plane

first, convert velocity in m/s

`\begin{gathered} v=\frac{400\text{ km}}{\text{ h}} \\ v=\frac{400\text{ km}}{\text{ h}}*\frac{1000\text{ m}}{\text{ km}}*\frac{1\text{ h}}{3600\text{ s}} \\ v=111.11\text{ m/s} \end{gathered}`

plugging all the values in the above formula, we get

`\begin{gathered} \tan\theta=\frac{(111.11\text{ m/s})^2}{2200\text{ m}*9.8\text{ m/s}^2} \\ \tan\theta=(12345.4321)/(21560) \\ \tan\theta=0.5726 \\ \theta=\tan^(-1)(0.5726) \\ \theta=29.79^(\degree) \end{gathered}`

Thus, the angle is

`29.79^(\degree)`