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Stationing of the PVC=117000 and length of the curve is 200m Find the Stationing of the PVI and PUT.

Mathematics

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Answer

11+100\text{11+100}

11+200\text{11+200}

Step-by-step solution

4 steps

This problem involves calculating the stationing of the Point of Vertical Intersection (PVI) and the Point of Vertical Tangency (PVT) given the stationing of the Point of Vertical Curvature (PVC) and the length of the vertical curve.

  1. Understand the given information.

    • Stationing of PVC (Point of Vertical Curvature) = 11+00011+000. This means 11000 m11000\, \text{m} from the starting reference point.
    • Length of the curve (LL) = 200 m200\, \text{m}.
  2. Determine the distance from PVC to PVI and from PVI to PVT.

    For a symmetrical vertical curve, the PVI is located at the midpoint of the curve. Therefore, the distance from PVC to PVI is half the curve length, and the distance from PVI to PVT is also half the curve length.
    Distance = L2=200 m2=100 m\frac{L}{2} = \frac{200\, \text{m}}{2} = 100\, \text{m}.

  3. Calculate the Stationing of PVI.

    The PVI (Point of Vertical Intersection) is located after the PVC. To find its stationing, add the distance calculated in Step 2 to the PVC stationing.
    Stationing of PVI = Stationing of PVC + L2\frac{L}{2}
    Stationing of PVI = 11000 m+100 m11000\, \text{m} + 100\, \text{m}
    Stationing of PVI = 11100 m11100\, \text{m}
    In stationing notation, this is 11+10011+100.

  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 + L2\frac{L}{2}
    Stationing of PVT = 11100 m+100 m11100\, \text{m} + 100\, \text{m}
    Stationing of PVT = 11200 m11200\, \text{m}
    In stationing notation, this is 11+20011+200.

    The Stationing of PVI is 11+100\boxed{\text{11+100}}.
    The Stationing of PVT is 11+200\boxed{\text{11+200}}.

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