Question

North West Down Suppose two divers start at the surface and establish the following coordinate system: x is to the West, y is to the North, and z is down. Diver 1 swims 55 ft. West, 36 ft. North, and then dives 25 ft. Diver 2 dives 15 ft., then swims East 20 ft. and then North 59 ft. a. Find the distance between diver 1 and the starting point. b. How far in each direction (West/East, North/South, Up/Down) must diver 1 swim to reach diver 2? C. How far in a straight line must diver 1 swim to reach diver 2? Deliverables 1. Provide a detailed problem analysis 2. Design an algorithm that can be used to solve the problem 3. Implement the algorithm in C++ You C++ program should prompt for the initial coordinates of diver 1 and diver 2. The prompts should be as clear as possible Submission Upload the detailed problem analysis, the algorithm and the Ctt source file to Canvas using the designated link NOTE: Make sure you upload the files using the designated link on Canvas before 4:35 pm. Remember, this is an exam. No submission after the deadilne, no submission via email. Failure to meet the submission deadline will result in a zero grade for part II. Any academic dishonesty will be dealt with accordingly. Choose only one problem

I need the algorithm and the c++ program

Answer 1

DETAILED PROBLEM ANALYSIS

The problem is a simple 3D vector problem and can be used by making use of vector arithmetics

Let the vector D1 = (x1, y1, z1) relative to 0

and vector D2 = (x2, y2, z2) relative to 0

where x is the distance travelled east, y is the distance travelled north and z is the distance travelled down for both divers D1 and D2

These data can be stored as integers x,y,z in the form of a structure vector

Let O = (0,0,0) be the origin.

1. The distance between 2 points is given as sqrt((x2-x1)² + (y2-y1)² + (z2-z1)²)

where the points are (x1,y1,z1) and (x2,y2,z2)

if one the points is initial point, the length of the vector is obtained.

2. Vector V1 - Vector V2 represents another vector from point D2 to point D1.

This creates a relative location between 2 points. if D2 is origin, no change is observed.

If V2 is the diver D1 and V1 the diver D2 we get (D2 - D1) a vector from diver D1 to diver D2. If D1 Traversing according to this new vector, D1 will eventually reach D2.

Note that Negative values only imply opposite direction which needs changes like East --> West, North --> South and Down --> Up

ALGORITHMS

// Global Variables and their Initial values //

vector O, D1, D2, I1, I2

X(O) <- Y(O) <- Z(O) <- 0

X(D1) <- Y(D1) <- Z(D1) <- 0

X(D2) <- Y(D2) <- Z(D2) <- 0

X(I2) <- Y(I2) <- Z(I2) <- 0

X(I2) <- Y(I2) <- Z(I2) <- 0

procedure MOVE_V(V, x, y, z)
    X(V) <- X(V) + x
    Y(V) <- Y(V) + y
    Y(V) <- Y(V) + z
end MOVE_V

procedure DISTANCE(V1, V2)
    x <- X(V2)-X(V1)
    y <- Y(V2)-Y(V1)
    z <- Z(V2)-Z(V1)
    return sqrt(x*x + y*y + z*z)
end DISTANCE

procedure MINUS(V1, V2)
    V <- NEWVECTOR()
    X(V) <- X(V1) - X(V2)
    Y(V) <- Y(V1) - Y(V2)
    Z(V) <- Z(V1) - Z(V2)
    return V
end MINUS

C++ PROGRAM

/* CODE BEGINS HERE */

#include <iostream>
#include <math.h>

struct vector
{
   int X;
   int Y;
   int Z;
};

vector O = { 0,0,0 };

// Current Position of Divers
vector D1 = { 0,0,0 };
vector D2 = { 0,0,0 };

// Start Points of Divers
vector I1 = { 0, 0, 0 };
vector I2 = { 0, 0, 0 };

vector MOVE(vector &V, int x, int y, int z)
{
   V.X += x;
   V.Y += y;
   V.Z += z;

   return V;
}

vector MINUS(vector V1, vector V2)
{
   vector V = {V1.X - V2.X, V1.Y - V2.Y, V1.Z - V2.Z};
   return V;
}

double DISTANCE(vector V1, vector V2)
{
   int x = V1.X - V2.X;
   int y = V1.Y - V2.Y;
   int z = V1.Z - V2.Z;

   return sqrt(x*x + y*y + z*z);
}

int main()
{
   int x, y, z;

   std::cout << "Enter initial x coordinate of Diver 1(-ve if East): ";
   std::cin >> x;
   std::cout << "Enter initial y coordinate of Diver 1(-ve if South): ";
   std::cin >> y;
   MOVE(D1, x, y, 0); // Both Starts From Surface
   MOVE(I1, x, y, 0);

   std::cout << "Enter initial x coordinate of Diver 2(-ve if East): ";
   std::cin >> x;
   std::cout << "Enter initial y coordinate of Diver 2(-ve if South): ";
   std::cin >> y;
   MOVE(D2, x, y, 0);
   MOVE(I2, x, y, 0);

   std::cout << "\nEnter Movement of Diver 1 in West Direction (-ve if East): ";
   std::cin >> x;
   std::cout << "Enter Movement of Diver 1 in North Direction (-ve if South): ";
   std::cin >> y;
   std::cout << "Enter Movement of Diver 1 in Down Direction (-ve if Up): ";
   std::cin >> z;
   MOVE(D1, x, y, z);

   std::cout << "\nEnter Movement of Diver 2 in West Direction (-ve if East): ";
   std::cin >> x;
   std::cout << "Enter Movement of Diver 2 in North Direction (-ve if South): ";
   std::cin >> y;
   std::cout << "Enter Movement of Diver 2 in Down Direction (-ve if Up): ";
   std::cin >> z;
   MOVE(D2, x, y, z);

   std::cout << "\n\nDistance Of Diver 1 From Starting Point = " << DISTANCE(D1, I1);

   vector path = MINUS(D2, D1);
   std::cout << "\n\nPath for Diver 1 to Reach D2 : \n";
   // If zero then no movement is required
   if (path.X > 0)
       std::cout << path.X << " towards West\n";
   else if (path.X > 0)
       std::cout << path.X*-1 << " towards East\n";
   if (path.Y > 0)
       std::cout << path.Y << " towards North\n";
   else if (path.Y > 0)
       std::cout << path.Y * -1 << " towards South\n";
   if (path.Z > 0)
       std::cout << path.Z << " towards Down\n";
   else if (path.Z > 0)
       std::cout << path.Z * -1 << " towards Up\n";

   std::cout << "\nDistance Diver 1 must travel to reach D2 = " << DISTANCE(path, O) << std::endl;

// Or DISTANCE(D1,D2)//

   return 0;
}

/* CODE ENDS HERE */

Answer 2

DETAILED PROBLEM ANALYSIS

The problem is a simple 3D vector problem and can be used by making use of vector arithmetics

Let the vector D1 = (x1, y1, z1) relative to 0

and vector D2 = (x2, y2, z2) relative to 0

where x is the distance travelled east, y is the distance travelled north and z is the distance travelled down for both divers D1 and D2

These data can be stored as integers x,y,z in the form of a structure vector

Let O = (0,0,0) be the origin.

1. The distance between 2 points is given as sqrt((x2-x1)² + (y2-y1)² + (z2-z1)²)

where the points are (x1,y1,z1) and (x2,y2,z2)

if one the points is initial point, the length of the vector is obtained.

2. Vector V1 - Vector V2 represents another vector from point D2 to point D1.

This creates a relative location between 2 points. if D2 is origin, no change is observed.

If V2 is the diver D1 and V1 the diver D2 we get (D2 - D1) a vector from diver D1 to diver D2. If D1 Traversing according to this new vector, D1 will eventually reach D2.

Note that Negative values only imply opposite direction which needs changes like East --> West, North --> South and Down --> Up

ALGORITHMS

// Global Variables and their Initial values //

vector O, D1, D2, I1, I2

X(O) <- Y(O) <- Z(O) <- 0

X(D1) <- Y(D1) <- Z(D1) <- 0

X(D2) <- Y(D2) <- Z(D2) <- 0

X(I2) <- Y(I2) <- Z(I2) <- 0

X(I2) <- Y(I2) <- Z(I2) <- 0

procedure MOVE_V(V, x, y, z)
    X(V) <- X(V) + x
    Y(V) <- Y(V) + y
    Y(V) <- Y(V) + z
end MOVE_V

procedure DISTANCE(V1, V2)
    x <- X(V2)-X(V1)
    y <- Y(V2)-Y(V1)
    z <- Z(V2)-Z(V1)
    return sqrt(x*x + y*y + z*z)
end DISTANCE

procedure MINUS(V1, V2)
    V <- NEWVECTOR()
    X(V) <- X(V1) - X(V2)
    Y(V) <- Y(V1) - Y(V2)
    Z(V) <- Z(V1) - Z(V2)
    return V
end MINUS

C++ PROGRAM

/* CODE BEGINS HERE */

#include <iostream>
#include <math.h>

struct vector
{
   int X;
   int Y;
   int Z;
};

vector O = { 0,0,0 };

// Current Position of Divers
vector D1 = { 0,0,0 };
vector D2 = { 0,0,0 };

// Start Points of Divers
vector I1 = { 0, 0, 0 };
vector I2 = { 0, 0, 0 };

vector MOVE(vector &V, int x, int y, int z)
{
   V.X += x;
   V.Y += y;
   V.Z += z;

   return V;
}

vector MINUS(vector V1, vector V2)
{
   vector V = {V1.X - V2.X, V1.Y - V2.Y, V1.Z - V2.Z};
   return V;
}

double DISTANCE(vector V1, vector V2)
{
   int x = V1.X - V2.X;
   int y = V1.Y - V2.Y;
   int z = V1.Z - V2.Z;

   return sqrt(x*x + y*y + z*z);
}

int main()
{
   int x, y, z;

   std::cout << "Enter initial x coordinate of Diver 1(-ve if East): ";
   std::cin >> x;
   std::cout << "Enter initial y coordinate of Diver 1(-ve if South): ";
   std::cin >> y;
   MOVE(D1, x, y, 0); // Both Starts From Surface
   MOVE(I1, x, y, 0);

   std::cout << "Enter initial x coordinate of Diver 2(-ve if East): ";
   std::cin >> x;
   std::cout << "Enter initial y coordinate of Diver 2(-ve if South): ";
   std::cin >> y;
   MOVE(D2, x, y, 0);
   MOVE(I2, x, y, 0);

   std::cout << "\nEnter Movement of Diver 1 in West Direction (-ve if East): ";
   std::cin >> x;
   std::cout << "Enter Movement of Diver 1 in North Direction (-ve if South): ";
   std::cin >> y;
   std::cout << "Enter Movement of Diver 1 in Down Direction (-ve if Up): ";
   std::cin >> z;
   MOVE(D1, x, y, z);

   std::cout << "\nEnter Movement of Diver 2 in West Direction (-ve if East): ";
   std::cin >> x;
   std::cout << "Enter Movement of Diver 2 in North Direction (-ve if South): ";
   std::cin >> y;
   std::cout << "Enter Movement of Diver 2 in Down Direction (-ve if Up): ";
   std::cin >> z;
   MOVE(D2, x, y, z);

   std::cout << "\n\nDistance Of Diver 1 From Starting Point = " << DISTANCE(D1, I1);

   vector path = MINUS(D2, D1);
   std::cout << "\n\nPath for Diver 1 to Reach D2 : \n";
   // If zero then no movement is required
   if (path.X > 0)
       std::cout << path.X << " towards West\n";
   else if (path.X > 0)
       std::cout << path.X*-1 << " towards East\n";
   if (path.Y > 0)
       std::cout << path.Y << " towards North\n";
   else if (path.Y > 0)
       std::cout << path.Y * -1 << " towards South\n";
   if (path.Z > 0)
       std::cout << path.Z << " towards Down\n";
   else if (path.Z > 0)
       std::cout << path.Z * -1 << " towards Up\n";

   std::cout << "\nDistance Diver 1 must travel to reach D2 = " << DISTANCE(path, O) << std::endl;

// Or DISTANCE(D1,D2)//

   return 0;
}

/* CODE ENDS HERE */

Microsoft Visual Studio Debug Console Enter initial x coordinate of Diver 1(-ve if East): 1 Enter initial y coordinate of Diver 1(-ve if South): 2 Enter initial x coordinate of Diver 2(-ve if East): -4 Enter initial y coordinate of Diver 2(-ve if South): 8 Enter Movement of Diver 1 in West Direction (-ve if East): 55 Enter Movement of Diver 1 in North Direction (-ve if South): 36 Enter Movement of Diver 1 in Down Direction (-ve if Up): 25 Enter Movement of Diver 2 in West Direction (-ve if East): -20 Enter Movement of Diver 2 in North Direction (-ve if South): 59 Enter Movement of Diver 2 in Down Direction (-ve if Up): 15 Distance Of Diver 1 From Starting Point = 70.3278 Path for Diver 1 to Reach D2 : 29 towards North Distance Diver 1 must travel to reach D2 = 85.6796 C:\Users\avjef\source\repos\Activity Working\Debug\Activity Working.exe (process 3080) exited with code 0. To automatically close the console when debugging stops, enable Tools->Options ->Debugging->Automatically close the conso le when debugging stops. Press any key to close this window ...