To help prevent future collisions between cars and trains, an at-grade crossing of a rail road by a country road is being redesigned so that the county road will pass
underneath the tracks. Currently the vertical alignment of the county road consists of an equal tangents crest vertical curve joining a 4% upgrade to a 3%
downgrade. The existing vertical curve is 450 feet long, the PVC of this curve is at station 48+24.00, and the elevation of the PVC is 1591.00 feet. The
centerline of the train tracks is at station 51+50.00. Your job is to find the shortest vertical curve that provides 20 feet of clearance between the new county
road and the train tracks, and to make a preliminary estimate of the cut that will be needed to construct the new curve.