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Ok... What am i doing wrong here, i don't seem to be able to find the right answer to this problem.

After i drew a free-body diagram, the centripetal force, a component of the Normal force is what is letting the car turn successfully.

so, cos theta *g*m = the Normal force.

The x component of the Normal force is providing the centripetal acceleration.

the line of the x component of the Normal force and the horizontal line of the ground is parallel so i figured out the x component as sin theta * Normal force

so sin theta * cos theta *g*m = m * 11.111m/s^2/30

using the trig identity sin2theta = 2sintheta*cos theta

sin 2 theta/2 * g = 4.11m/s^2

theta = 29 degrees

This is not the correct answer. The correct answer is 23 degrees. Can some one please explain my error. Thanks in advance...