A race car driving on a banked track that makes an angle \(\theta\) with the horizontal rounds a curve for which the radius of curvature is R.

(a) As described in Problem 12, there is one speed \(v_{\text {critical }}\) at which friction is not needed to keep the car on the track. What is that speed in terms of \(\theta\) and \(R\) ?

(b) If the coefficient of friction between tires and road is \(\mu\), what maximum speed can the car have without going into a skid when taking the curve?