Dead Man's Curve

You are working for the Florida Department of Transportation when your group gets the assignment to redesign two curves on I-10 where there were several accidents last year due to ice on the road. The two turns have radii of 100 m and 200 m, respectively. Since friction is negligible under icy conditions, this means the turns must be banked. Your boss wants you to figure out the angle at which the curves should be banked (relative to the horizontal) to make sure cars can get through the turn safely at the speed limit of 70 mph.