This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
This problem involves calculating the stationing of the Point of Vertical Curvature (PVC) and the Point of Vertical Tangency (PVT) given the stationing of the Point of Vertical Intersection (PVI) and the length of the vertical curve. Step 1: Understand the given information. Stationing of PVI (Point of Vertical Intersection) = 11+700. This means 11700\, m from the starting reference point. Length of the curve (L) = 200\, m. Step 2: Determine the distance from PVI to PVC and from PVI to PVT. For a symmetrical vertical curve, the PVI is located at the midpoint of the curve. Therefore, the distance from PVI to PVC is half the curve length, and the distance from PVI to PVT is also half the curve length. Distance = (L)/(2) = 200\, m2 = 100\, m. Step 3: Calculate the Stationing of PVC. The PVC (Point of Vertical Curvature) is located before the PVI. To find its stationing, subtract the distance calculated in Step 2 from the PVI stationing. Stationing of PVC = Stationing of PVI - (L)/(2) Stationing of PVC = 11700\, m - 100\, m Stationing of PVC = 11600\, m In stationing notation, this is 11+600. Step 4: Calculate the Stationing of PVT. The PVT (Point of Vertical Tangency) is located after the PVI. To find its stationing, add the distance calculated in Step 2 to the PVI stationing. Stationing of PVT = Stationing of PVI + (L)/(2) Stationing of PVT = 11700\, m + 100\, m Stationing of PVT = 11800\, m In stationing notation, this is 11+800. The Stationing of PVC is 11+600. The Stationing of PVT is 11+800. 3 done, 2 left today. You're making progress.