## Essential University Physics: Volume 1 (3rd Edition)

$\mu = \frac{v^2}{gr} - tan(tan^{-1}(\frac{v_0^2}{rg}))$
We find the angle of the road based on the maximum posted speed. Thus, we obtain: $\theta = tan^{-1}(\frac{v_0^2}{rg})$ We also know: $mgcos\theta \mu+mgsin\theta=\frac{mv^2}{r}$ Thus, we find an expression for $\mu$: $\mu=\frac{\frac{v^2}{r}-gsin\theta}{gcos\theta}$ $\mu = \frac{v^2}{gr} - tan\theta$ Plugging in the value of theta gives: $\mu = \frac{v^2}{gr} - tan(tan^{-1}(\frac{v_0^2}{rg}))$