The figure shows two possible paths for negotiating an unbanked turn on a horizontal por...

The figure shows two possible paths for negotiating an unbanked turn on a horizontal portion of a race course. Path A-A follows the centerline of the road and has a radius of curvature ρ_A = 85 m, while path B-B uses the width of the road to good advantage in increasing the radius of curvature to ρ_B = 200 m. If the drivers limit their speeds in their curves so that the lateral acceleration does not exceed 0.8g, determine the maximum speed for each path.