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IceJOKER [234]
3 years ago
8

1. A vertical curve joins a -1.2% grade to a +0.8% grade. The two grades intersect at station 75 + 00 and elevation 50.90 m abov

e sea level. The centerline of the roadway must clear a pipe located at station 75 + 40 by 0.80 m. The elevation of the top of the pipe is 51.10 m above sea level. What is the minimum length of the vertical curve that can be used?
Engineering
1 answer:
Aneli [31]3 years ago
6 0

Answer:

The minimum length of the vertical curve that can be used is 416.63 m

Explanation:

g₁ = -1.2% , g₂ = 0.8%

Station (Sta) = 75 + 00

Elevation (Ele) = 50.90 m

x₀ = Sta(VPC) = Sta(VPI) - L/2 ⇒ 7500 - L/2

y₀ = Ele(VPC) = Ele(VPI) - g₁L/2 == 50.90 - (-0.012)L/2 ⇒ 50.90 + 0.012L/2

at Sta 75+40, x = 7540 -x₀ = 40 + L/2

at Ele, y = 51.10 + C = 51.10 + 0.80 ⇒ y = 51.90 m

Equation of vertical curve is

y = y_0 + g_1x + \frac{g_2-g_1}{2L}x^2

Substituting the values for x and y

51.90 = (50.90 + \frac{0.012}{2}L)+(-0.012)(40+\frac{L}{2)}+\frac{(0.8+1.2)}{100*2L}*(40+\frac{L}{2})^2

0 = -1.48 + \frac{0.02}{2L}(1600+\frac{L^2}{4}+40L)

0 = -148L + 1600 + \frac{L^2}{4} + 40L

Solving : L = 416.63 m

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IN JAVA,
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Answer:

Explanation:

Code:

import java.io.File;

import java.io.FileWriter;

import java.io.IOException;

import java.util.Scanner;

public class Knapsack {

 

  public static void knapsack(int wk[], int pr[], int W, String ofile) throws IOException

  {

      int i, w;

      int[][] Ksack = new int[wk.length + 1][W + 1];

     

      for (i = 0; i <= wk.length; i++) {

  for (w = 0; w <= W; w++) {

  if (i == 0 || w == 0)

  Ksack[i][w] = 0;

  else if (wk[i - 1] <= w)

  Ksack[i][w] = Math.max(pr[i - 1] + Ksack[i - 1][w - wk[i - 1]], Ksack[i - 1][w]);

  else

  Ksack[i][w] = Ksack[i - 1][w];

  }

  }

     

      int maxProfit = Ksack[wk.length][W];

      int tempProfit = maxProfit;

      int count = 0;

      w = W;

      int[] projectIncluded = new int[1000];

      for (i = wk.length; i > 0 && tempProfit > 0; i--) {

         

      if (tempProfit == Ksack[i - 1][w])

      continue;    

      else {

          projectIncluded[count++] = i-1;

      tempProfit = tempProfit - pr[i - 1];

      w = w - wk[i - 1];

      }

     

      FileWriter f =new FileWriter("C:\\Users\\gshubhita\\Desktop\\"+ ofile);

      f.write("Number of projects available: "+ wk.length+ "\r\n");

      f.write("Available employee work weeks: "+ W + "\r\n");

      f.write("Number of projects chosen: "+ count + "\r\n");

      f.write("Total profit: "+ maxProfit + "\r\n");

     

  for (int j = 0; j < count; j++)

  f.write("\nProject"+ projectIncluded[j] +" " +wk[projectIncluded[j]]+ " "+ pr[projectIncluded[j]] + "\r\n");

  f.close();

      }    

  }

 

  public static void main(String[] args) throws Exception

  {

      Scanner sc = new Scanner(System.in);

      System.out.print("Enter the number of available employee work weeks: ");

      int avbWeeks = sc.nextInt();

      System.out.print("Enter the name of input file: ");

  String inputFile = sc.next();

      System.out.print("Enter the name of output file: ");

      String outputFile = sc.next();

      System.out.print("Number of projects = ");

      int projects = sc.nextInt();

      int[] workWeeks = new int[projects];

      int[] profit = new int[projects];

     

      File file = new File("C:\\Users\\gshubhita\\Desktop\\" + inputFile);

  Scanner fl = new Scanner(file);

 

  int count = 0;

  while (fl.hasNextLine()){

  String line = fl.nextLine();

  String[] x = line.split(" ");

  workWeeks[count] = Integer.parseInt(x[1]);

  profit[count] = Integer.parseInt(x[2]);

  count++;

  }

 

  knapsack(workWeeks, profit, avbWeeks, outputFile);

  }

}

Console Output:

Enter the number of available employee work weeks: 10

Enter the name of input file: input.txt

Enter the name of output file: output.txt

Number of projects = 4

Output.txt:

Number of projects available: 4

Available employee work weeks: 10

Number of projects chosen: 2

Total profit: 46

Project2 4 16

Project0 6 30

8 0
3 years ago
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