A car goes around a curve on a road that is banked at an angle of 30 degrees. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 24.0 m/s. WHAT IS THE RADIUS OF THE CURVE?

Answer 1

Let
g = acceleration due to gravity = 9.8 m/s²
r = the radius in m,
m = mass of car in kg
v = tangential velocity = 24 m/s
θ = superelevation angle = 30°

horizontal component, H
= mv²/r

vertical component, V
= mg

If the superelevation is perfectly matched to the speed of the car, then
tan(θ) = V/H
solve for r.
I get about 34 m.