Centripetal motion, how to find radius?

[cruisx]

Homework Statement

Hi guys, i need some help solving the following question.

An Airplane is flying in a Horizontal circle at speed of 620km/h. If the wings of the plane are tilted 35 degrees to the horizontal, what is the radius of the circle in which the plane is flying? Assume that the required force is provided entirely by an aerodynamic lift that is perpendicular to the wing surface.

Homework Equations

The Attempt at a Solution

I know that if i had time i could find the radius by using R = vT/2pi But i don't have that so how would i go about solving this Problem? Also what can i do with that angle?

 

[cepheid]

A certain amount of centripetal acceleration is required in order to keep the plane in a circle going at that speed at a certain radius. In fact, you should know how the centripetal acceleration is related to the speed and radius of the circle.

As for the angle, the lift force is what is providing the centripetal force. However, because the wing is tilted at a certain angle, and the lift force is perpendicular to it, only a certain component of the lift force will be pointing in the "centripetal" direction. You can calculate what that component is.

 

[cruisx]

Ok thank you, so i came up with the following, is this correct?
I got the equation m(v²/R) = mgtan$$\theta$$
then i changed that to this as both masses cancel out.

r = V²/gtan35

and my answer was

4750.8m.

Is this correct?

 

[cepheid]

I agree with your formula. My answer is less than yours by 432.8 m.

 

[cruisx]

I agree with your formula. My answer is less than yours by 432.8 m.

Oops i think i used 650km instead of 620km/h. I got this

4321.29m

Correct?

 

[cepheid]

Seems closer. Like I said in my previous post, I got ~ 4318 m