Acar drives over the top of a hill that has a radius of 30 m . part a what maximum speed can the car have without flying off the road at the top of the hill?

If we assume the hill is perfectly circular, then we can assume that the cars motion about the hill is centripetal, and therefore the acceleration of the car can be given by v^2/r. In order for the car to not fly off the hill, the centripetal acceleration of the car cannot exceed the acceleration due to gravity, 9.81 m/s^2, therefore for maximum acceleration g=v^2/r, and rearranging this sqrt(g*r)=v. v=sqrt(9.81*30) m/s