Uniform Circular Motion and Centripetal Force

Hey guys, first post here! Hoping to get a little help.
1. The problem statement, all variables and given/known data

You are a traffic safety engineer in charge of determining safe speeds for roads. A particular banked curve has a radius of 11.0 meters and is banked at an angle of 8.00°. The coefficient of static friction between common tires and this road is 0.870. What is the maximum speed that a car can drive this curve? Use both the bank of the curve and the friction on the tires in determining your answer.

2. Relevant equations

3. The attempt at a solution

So what I did was split the force of gravity, mgcos8 in the direction perpendicular to the ramp and mgsin8 parallel. Also, the force of friction towards the center of rotation and set all forces towards the center of rotation to mv^2/r.

Essentially, I had mgsin8 + (μ X mg X cos8)=mv^2/r.

Common factor of m cancels and I solve for V as everything else is given. I receive an answer of 10.4 m/s. The correct answer is apparently 11.1 m/s, so close, but not close enough for a rounding issue I believe. My only other guess is that somehow I’ve split the vector wrong. Any help’s much appreciated, thanks very much in advance.


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