To illustrate, calculate the speed at which a 100 m radius curve banked at 65.0 degrees should be driven if the road is frictionless, given tan(65.0 degrees) is about 2.14.

1. For an ideally banked curve, tan(theta) = v^2 / (r*g), so solving for speed gives v = the square root of (r*g*tan(theta)). 2. Substituting the known values, v = the square root of (100 m)(9.80 m/s^2)(2.14). 3. Multiplying inside the square root gives 100 times 9.80 times 2.14, which is about 2097.2 m^2/s^2. 4. Taking the square root of 2097.2 gives v = 45.8 m/s. 5. This banking angle allows a much higher safe speed than a gentler curve would, which is why race tracks use steep banking on tight curves. 6. 213 m/s would come from forgetting to take the square root, 97.9 m/s from doubling the radius by mistake, and 14.6 m/s from taking the square root of only the tangent term. _Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.3 Centripetal Force_