A car traveling around a banked curve must have some margin of error. If the spe

Question

A car traveling around a banked curve must have some margin of error. If the speed limit on a curve is set to 35 mph (15.64 m/s) is banked at 25 degrees, has a radius of 61m and the coefficient of static friction between rubber tires and a wet road is .25, what is the maximum speed that can be attained before the car fails to negotiate the curve?

I already solved it, but I'm not sure about my answer. If you could check it, give the actual answer, and explain how you got that answer, I would greatly appreciate it.

This is how I solved it:
(mv^2)/r= m(coefficient of friction)g+ mgsin(25)
v^2/r= (coefficient)g+ gsin25
I then used the givens to solve the right side of the equation, and then multiplied it by r, and then found the square root of that answer. I ended up with 20.0 m/s (with sig figs). Is this right? What did I do wrong. By the way, I'm in a high school AP physics class, so we don't use calculus.

Explanation / Answer

From the definition of banking angle,

Tan = V^2/rg

Tan25 = V^2/61*9.8

V = 16.69 m/s

the maximum speed that can be attained before the car fails to negotiate the curve is 16.69 m/s.

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