Kennesaw State University CS 4491 Assignment 2

Kennesaw State University

Department of Computer Science

Advanced Topic in Computer Science CS 4491/2

Assignment #2: Computer Modeling

Dalibor Labudovic

01/29/2013

Initial Problem Statement:

1.) Assume that the initial velocity, v0, of the free-falling object is not zero. Develop a computational model (in the C language) that computes the time the object takes to reach ground level and the vertical velocity at that time instance, given the initial height, y0.

2.) A large tent is to be set up for a special arts display in the main city park. The tent material is basically a circular canvas; the tent size can be adjusted by increasing or decreasing the distance from the center to the edge of the canvas, varying from 5 feet to 35 feet. The cost of the event will be paid based on the circular area occupied, $1:25 per square foot. Develop a computational model that takes several values of the distance from the center to the outer edge of the canvas (the radius) and provide the cost for the event.

Summary and Purpose of the Assignment Activity:

The purpose of the assignment is to critically analyze and abstract the problem. With an abstraction of the problem, a mathematical model can be created. Working with the mathematical algorithm and principles of software development, a computational model is developed. Once a reasonable computational model is reached then I was able to constructed, compiled, tested and deployed the program.

Detail Description of the Solution Used in the Project:

1. To develop a C program to calculate the time and velocity for a free falling object, I initially started with a mathematical model of the problem. First I analyzed the given variables. The distance is given and constant is acceleration. The formula for distance on free falling object is , where a, as a double value, is acceleration at -9.8 m/s , d, as a double value, is distance in meters, and t , as a double value, is for time in seconds. The manipulated mathematical model for finding time of a free falling object is: . The formula for calculating the velocity of the object is , where v , a double value, is velocity in m/ and a, as a double value, is for constant acceleration,- 9.8 m/ and t , as a double value, is for time in seconds. Mathematical model provides a clear picture to the components required for the computational model. The variable d is needed from the end user. The library math.h is required to compute the algorithms. The computational model will implement the mathematical formulation . The main function will execute the formula for time, . Once the time has been calculated then the function will resume to calculate the velocity using formula, .
2. To develop a computational model for determining the setup cost of tent display for marketing. The tent size ranges from 5ft to 35 ft. To calculate the area, a double value, of the tent, I will use a mathematical formula, area of a circle, . The constant is PI is a double value of 3.14159 and the r is a double value as the radius , which ranges from 5ft to 35ft. Once the area of the tent is calculated, we apply the mathematical formula , for the cost, at $1.25 per square feet.

Table of Results:

1.) In the C program of a free-falling object, the results are:

Source File:

#include <stdio.h>

#include <math.h>

int main(){

double a = -9.8;//accelertion due to gravity

double x;//distance

double t;//time

double v;//initial velocity

double vf;//final velocity

//user input

printf("\nThis program calculates time and velocity for free falling object\n");

printf("\nProvide distance in meters:");

scanf("%lf", &x);

printf("\nProvide Initial Velocity in m/s: ");

scanf("%lf", &v);

//Calculate final velocity

vf = sqrt(pow(v,2) +( 2 * a * x));

//calculate time

t = (vf - v)/(a);

//print output

printf("\nWith initial velocity of %g m/a and distance of %g meters", v,x);

printf("\nThe finail velocity is %g m/s and time it took to fall is %g seconds", vf, t)

return 0;

}

2.)

Source File:
#include <stdio.h>
#include <math.h>

int main(){

//data structure

double area;

double radius;

double tentcost;

const double PI = 3.14159;

//user input

printf("\nEnter tent radius 5-35ft\n");

scanf("%lf", &radius);

if (radius < 4){

printf("Error, radius too small");

}

else if (radius > 35){

printf("Error, radius too large");

}

else{

//calcualte area

area = PI * pow(radius,2);

//calculate cost

tentcost = area * 1.25;

//print results

printf("\nTotal area is %g sqft", area);

printf("\nTotal cost at $1.25/sqft is $%g", tentcost);

}

return 0;

}

Discussion of How the System Modeled can be Improved and Extended to Include other Services:

1.) The free-falling object program can be improved by using an animation of the object falling by using a GUI and introducing an option of initial velocity and final velocity. The program could also include an option for drag co-efficiency calculations.

2.) The cost of the tent computational model could be improved with an introduction of a seek bar in a GUI environment.

Comments and Conclusion:

The interesting part of the project is distinguishing the differences between the mathematical model and computational model. With more complex problems, the use of translating from mathematical model to computational model will become a required skill.

List of References:

"Area of a Circle." Area of a Circle. N.p., n.d. Web. 30 Jan. 2013.

"Kinematic Equations and Free Fall." Kinematic Equations and Free Fall. N.p., n.d. Web. 30 Jan. 2013.

Script:

1. Script File

Script started on Sat 09 Feb 2013 11:22:42 PM EST

[?1l>[dlabudov@cs3 ~]$ gcc -Wall freefall.c -lm

[dlabudov@cs3 ~]$ ./a.out

This program calculates time and velocity for free falling object

Provide distance in meters:-20

Provide Initial Velocity in m/s: 6

With initial velocity of 6 m/a and distance of -20 meters

The finail velocity is 20.6882 m/s and time it took to fall is -1.49879 seconds[dlabudov@cs3 ~]$ exit

exit

Script done on Sat 09 Feb 2013 10:31:35 PM EST

2. Script File

Script started on Sat 09 Feb 2013 11:22:42 PM EST

[?1l>[dlabudov@cs3 ~]$ gcc -Wall tentcost.c -lm

[dlabudov@cs3 ~]$ ./a.out

Enter tent radius 5-35ft

10

Total area is 314.159 sqft

Total cost at $1.25/sqft is $392.699[dlabudov@cs3 ~]$ ./a.out

Enter tent radius 5-35ft

2

Error, radius too small[dlabudov@cs3 ~]$ ./a.out

Enter tent radius 5-35ft

40

Error, radius too large[dlabudov@cs3 ~]$ exit

exit

Script done on Sat 09 Feb 2013 11:23:34 PM EST