You want to design a curve, with a radius of curvature of 35.0 m, so that a car can turn at a velocity of 15 m/s on it without depending on friction. At what angle must the road be banked?
No tire friction is required if the force on tires at the road surface, Fn, is normal to the surface. That requires
Fn sinA = M*V^2/R (to provide the centripetal force), and
Fn cosA = M*g
(to balance the weight).
A is the banking angle.
This leads to
tanA = V^2/(R*g)