A car moves along a curved road of diameter 2 km. If the maximum velocity for safe driving on this path is 30 m/s, at what angle has the road been banked? (Ignore friction.)

The maximum velocity in a banked road, ignoring friction, is given by;

v = Sqrt (Rg tan ∅), where R = Radius of the curved road = 2*1000/2 = 1000 m, g = gravitational acceleration = 9.81 m/s^2, ∅ = Angle of bank.

Substituting;

30 m/s = Sqrt (1000*9.81*tan∅)

30^2 = 1000*9.81*tan∅

tan ∅ = (30^2) / (1000*9.81) = 0.0917

∅ = tan^-1 (0.0917) = 5.24°

Therefore, the road has been banked at 5.24°.