Plane flying at an angle, trying to find radius

[I_LuV_FiZiX]

Homework Statement

To change the direction of the plane, its wings are banked. If the wings of the plane are banked 50.0° to the horizontal, what is the radius of the circle in which the plane will be flying? Assume that the speed remains 480.0 km/h during the turn and that the magnitude of the lift provided by the wings is unchanged.

Homework Equations

m = 13900kg (given previous to this problem) but I do not think this comes into play

The Attempt at a Solution

I said that the forceof the lift = L. the sum of forces in the y direction = Lcos50 = mg. The sum of forces in the x direction = Lsin50 = (mv^2)/r. Solving both equations for L and then setting these expressions equal to each other, I eventually came to r = (v^2)/gtan50, giving me an answer of 19,707km. The computer keeps telling me I am incorrect.

Any help would be appreciated

 

[Doc Al]

Be careful with units. That speed is given in km/hour--convert to standard units.

 

[I_LuV_FiZiX]

still wrong

 

[I_LuV_FiZiX]

that gave me an answer of 1521m, which seems kind of small anyway

 

[Doc Al]

that gave me an answer of 1521m, which seems kind of small anyway

Looks right to me.

 

[I_LuV_FiZiX]

so do you think that it could possibly be an error with the computer? I can't see any mistake I have made.

 

[Doc Al]

It wouldn't surprise me, as those systems can be fussy. What units does it want? How many significant figures?

 

[I_LuV_FiZiX]

It does no specify what units it wants, or how many significant figures. I have tried many combinations of both.

 

[Doc Al]

Oops. I missed the implication of this:

Assume that the speed remains 480.0 km/h during the turn and that the magnitude of the lift provided by the wings is unchanged.

So the following is incorrect:

I said that the forceof the lift = L. the sum of forces in the y direction = Lcos50 = mg.

This (the last sentence) is not true. Once the plane banks there is no longer vertical equilibrium.

My bad!

Your bad: Please post the entire problem.

(Thanks to alphysicist for waking me up! )