To determine the coefficient of static friction required for a car to navigate a banked curve without skidding, the discussion revolves around the relationship between speed, radius, and banking angle. The initial calculations used the formula for static friction, but multiple attempts yielded incorrect values. The correct approach involves analyzing the forces acting on the car, including gravitational force, normal force, and frictional force, while applying Newton's second law. Ultimately, the coefficient of static friction needed for the car traveling at 91.2 km/hr is calculated to be approximately 0.296. This solution highlights the importance of understanding the dynamics of motion on banked curves.