Engineering a highway curve. If a car goes through a curve too fast, the car tends to slide out of the curve. A frictional force acts on a fast car to oppose the tendency to slide out of the curve. Consider a circular curve of radius R and bank angle θ, where the coefficient of static friction between the tires and the road is μs. A car is driven around the curve as shown in the figure. Find an expression for the maximum speed, Vmax, that the car can go around the curve without sliding out, in terms of R, θ, and μs. Evaluate Vmax for a radius of R = 174 m, a bank angle of θ = 14.0°, and coefficient of static friction μs = 0.503. Convert your answer to km/hr.

Question

Engineering a highway curve.  If a car goes through a curve too fast, the car tends to slide out of the curve.  A frictional force acts on a fast car to oppose the tendency to slide out of the curve.  Consider a circular curve of radius R and bank angle θ, where the coefficient of static friction between the tires and the road is μs.  A car is driven around the curve as shown in the figure.  Find an expression for the maximum speed, Vmax, that the car can go around the curve without sliding out, in terms of R, θ, and μs.  Evaluate Vmax for a radius of R = 174 m, a bank angle of θ = 14.0°, and coefficient of static friction μs = 0.503.  Convert your answer to km/hr.

So the answer was 138km/hr, but I am so confused on the steps to get to the answers! Can someone please explain it to me step-by-step?