create a function file that calculates the trajectory of a projectile. The inputs to the function are the initial velocity and the angle at which the projectile is fired. The outputs from the function are the maximum height and distance. In addition, the function generates a plot of the trajectory. Use the function to calculate the trajectory of a projectile that is fired at a velocity of 230 m/sec at an angle of 39deg.

Problem: 
                              create a function file that calculates the trajectory of a projectile. The inputs to the function are the initial velocity and the angle at which the projectile is fired. The outputs from the function are the maximum height and distance. In addition, the function generates a plot of the trajectory. Use the function to calculate the trajectory of a projectile that is fired at a velocity of 230 m/sec at an angle of 39deg.


 USING MATLAB SOFTWARE Version 7.0


SOLUTION:-

%Write it in script file
function[hmax,dmax]=trajectory(V0,theta)              
g=9.81;
V0x=V0*cos(theta);
V0y=V0*sin(theta);
thmax=V0y/g;
hmax=V0y^2/(2*g);
ttotal=2*thmax
dmax=V0x*ttotal
 % creating a trajectory plot
tplot=linspace(0,ttotal,200);
x=V0x*tplot;
y=V0y*tplot-0.5*g*tplot.^2;
plot(x,y)
xlabel('distance (mt)')
ylabel('height(mt)')
title('projectile of Rocket')



>> [height distance]=trajectory(230,39)        %In command window

ttotal =

   45.1933


dmax =

  2.7716e+003


height =

  2.5045e+003


distance =

  2.7716e+003




Trajectory of profile

The co-efficient of friction mu can be determined in an experiment by measuring the force F required to move a mass m. when F is measured and m is known the coefficient of friction can be calculated by mu=F/mg (g=9.81 m/sec2) results from measuring F in six tests are given in the table below. Determine the coefficient of friction in each test, and average from all tests.

Problem: 
                         The co-efficient of friction mu can be determined in an experiment by measuring the force F required to move a mass m. when F is measured and m is known the coefficient of friction can be calculated by mu=F/mg (g=9.81 m/sec2) results from measuring F in six tests are given in the table below. Determine the coefficient of friction in each test, and average from all tests.

    Test #
    1
    2
    3
    4
    5
    6
    Mass m-kg
    2
    4
    5
    10
    20
    50
    Force F -N
    12.5
    23.5
    30
    61
    117
    294


    USING MATLAB SOFTWARE

    SOLUTION:

    %IN COMMAND WINDOW

    >> m=[2 3 5 10 20 50];
    >>  f=[12.5 23.5 50 61 117 294];
    >>  mu=f./(m*9.8)

    mu =

        0.6378    0.7993    1.0204    0.6224    0.5969    0.6000

    >> mu_avg=mean(mu)

    mu_avg =

        0.7128

    Three forces are applied to a bracket as shown. Determine the total (equivalent) force applied to the barcket

    Problem:
            
    % Three forces are applied to a bracket as shown. Determine the total (equivalent) force applied to the barcket%


    %IN COMMAND WINDOW



    >> F1m=400;F2m=500;F3m=700;
    >> Th1=-20*pi/180;Th2=30*pi/180;Th3=143*pi/180;
    >> F1=F1m*[cos(Th1) sin(Th1)]

    F1 =

      375.8770 -136.8081

    >> F2=F2m*[cos(Th2) sin(Th2)]

    F2 =

      433.0127  250.0000

    >> F3=F3m*[cos(Th3) sin(Th3)]

    F3 =

     -559.0449  421.2705

    >> Ftotal=F1+F2+F3

    Ftotal =

      249.8449  534.4625

    >> Ftotalm=sqrt(Ftotal(1)^2+Ftotal(2)^2)

    Ftotalm =

      589.9768

    >> Th=(180/pi)*tan(Ftotal(2)/Ftotal(1))

    Th =

      -89.7088

    To determine Nearest of temp after 3 hours

    Problem: To determine Nearest of temp after 3 hours..

    >>% To determine Nearest of temp after 3 hours..%
    >> Ts=38;T0=120;K=0.45;t=3;
    >> T=round(Ts+(T0-Ts)*exp(-K*t))


    T =


    59

    A trigonometric identity is given by cos2(x/2)=(tanx+sinx)/2.tanx verify that the identity is correct by calculating each side of the equation substituting x=pi/5

     Problem :
             A trigonometric identity is given by cos2(x/2)=(tanx+sinx)/2.tanx verify that the identity is correct by calculating each side of the equation substituting x=pi/5


    >> %A trigonometric identity is given by cos2(x/2)=(tanx+sinx)/2.tanx verify that the identity is correct by calculating each side of the equation substituting x=pi/5%
    >> x=pi/5;
    >> LHS=cos(x/2)^2


    LHS =


    0.9045


    >> RHS=(tan(x)+sin(x))/(2*tan(x))


    RHS =


    0.9045

    c program to multiplication of two 3*3 matrices


        /* c program to multiplication of two 3*3 matrices*/

    #include<stdio.h>
    #include<conio.h>
    void main()
    {
         int m1[3][3],m2[3][3],prod[3][3];
         int i,j,k;
         clrscr();
          printf("enter the first matrix : \n");
            for(i=0;i<3;i++)
              for(j=0;j<3;j++)
               scanf("%d",&m1[i][j]);
         printf("enter 2nd matrix : \n");
             for(i=0;i<3;i++)
               for(j=0;j<3;j++)
                scanf("%d",&m2[i][j]);

    /* multiplication of matrix */
          for(i=0;i<3;i++)
         for(j=0;j<3;j++)

         {
           prod[i][j]=0;
           for(k=0;k<3;k++)
           prod[i][j]=prod[i][j]+m2[i][k]*m2[k][j];
        }

      
             printf("\n\n product matrix\n");
                for(i=0;i<3;i++)
            {
                  for(j=0;j<3;j++)
                         printf("%d\t",prod[i][j]);
                           printf("\n");
           }
    getch();
    }




    enter the first matrix
         4     4     4
         4     4     4
         4     4     4
    enter 2nd matrix
         4     4     4
         4     4     4
         4     4     4
    product matrix
        48    48    48
        48    48    48
        48    48    48

    c program to subtract two 3*3 matrices


    /*c program to subtract two 3*3 matrices*/
    #include<stdio.h>
    #include<conio.h>
    void main()
      {
        int m1[3][3],m2[3][3],msub[3][3];
        int i,j;
        clrscr();
        printf("type in 9 integer number of first matrix:\n");
        for(i=0;i<3;++i)
           for(j=0;j<3;++j)
                       scanf("%d",&m1[i][j]);
        printf("\n type in 9 integer number of first matrix:\n");
        for(i=0;i<3;++i)
           for(j=0;j<3;++j)
                       scanf("%d",&m2[i][j]);

    /*matrix subtraction proceeds as follows...*/
       for(i=0;i<3;++i)
       for(j=0;j<3;++j)
           msub[i][j]=m1[i][j]-m2[i][j];
    /*subtraction matrix as follows...*/
       for(i=0;i<3;++i)
       {
       for(j=0;j<3;++j)
       printf("%3d",msub[i][j]);
       printf("\n");
       }
    getch();
    }



    type in 9 integer number first matrix:
    1 2 3
    3 2 1
    4 5 6

    type in 9 integer number of second matrix
    6 5 4
    3 2 1
    2 3 1


    Subscription of matrix
    -5 -3 -1
     0  0  0
     2  2  5


    c program to add two 3*3 matrices


    /*c program to add two 3*3 matrices*/
    #include<stdio.h>
    #include<conio.h>
    void main()
      {
        int m1[3][3],m2[3][3],madd[3][3],msub[3][3];
        int i,j;
        clrscr();
        printf("type in 9 integer number of first matrix:\n");
        for(i=0;i<3;++i)
           for(j=0;j<3;++j)
                       scanf("%d",&m1[i][j]);
        printf("\n type in 9 integer number of first matrix:\n");
        for(i=0;i<3;++i)
           for(j=0;j<3;++j)
                       scanf("%d",&m2[i][j]);

    /*matrix addition proceeds as follows...*/
        for(i=0;i<3;++i)
          for(j=0;j<3;++j)
                     madd[i][j]=m1[i][j]+m2[i][j];
    /*added matrix as follows...*/
       for(i=0;i<3;++i)
       {
       for(j=0;j<3;++j)
       printf("%3d",madd[i][j]);
       printf("\n");
       }
     getch();
    }





    type in 9 number of first matrix:
    1 2 3
    1 2 4
    2 1 3

    type in 9 integer number of first matrix:
    8 6 5
    7 8 9
    4 5 6

     9  8  8
     8 10 13
     6  6  9

    to arrange number descending using bubble sort technique


    /*to arrange number descending using bubble sort technique*/
    #include<stdio.h>
    #include<conio.h>
    void main()
    {
      int num[10];
      int loop,i;
      int last=10;
      int exchange;
      int temp;
     clrscr();

     printf("enter the 10 number\n");
     for(i=0;i<10;++i)
       scanf("%d",&num[i]);
    for(loop=0;loop<9;++loop)
    {
         exchange=0;
         for(i=0;i<(last-1);i++)
                     if(num[i]>num[i+1])
                        {
                          temp=num[i];
                          num[i]=num[i+1];
                          num[i+1]=temp;
                          exchange=exchange+1;
                        }
      if(exchange==0)
           break;
    else
          last=(last-1);
     }
    printf("number is in ascending order: \n");
    for(i=0;i<10;i++)
         printf("%d\n",num[i]);
    getch();
    }

    Enter the 10 number
    88
    0
    14
    1
    6
    9
    6
    94
    52
    22
    Number is in descending order:
    94
    88
    52
    22
    14
    9
    6
    6
    1
    0

    to arrange number ascending using bubble sort techniqu


                      /*to arrange number ascending using bubble sort technique*/
    #include<stdio.h>
    #include<conio.h>
    void main()
    {
      int num[10];
      int loop,i;
      int last=10;
      int exchange;
      int temp;
     clrscr();
     printf("enter the 10 number\n");
     for(i=0;i<10;++i)
       scanf("%d",&num[i]);
     for(loop=0;loop<9;++loop)
    {
        exchange=0;
         for(i=0;i<(last-1);i++)
                     if(num[i]<num[i+1])
                        {
                          temp=num[i];
                          num[i]=num[i+1];
                          num[i+1]=temp;
                          exchange=exchange+1;
                        }
      if(exchange==0)
           break;
     else
          last=(last-1);
     }
    printf("number is in descending order: \n");
    for(i=0;i<10;i++)
         printf("%d\n",num[i]);
    getch();
    }


    Enter  the 10 number
    25
    20
    6
    14
    12
    32
    4
    6
    8
    9
    Number is in ascending order:
    4
    6
    6
    8
    9
    12
    14
    20
    25
    32

    sum and average of 3 numbers


    /*sum and average of 3 numbers*/
    #include <stdio.h>
    #include <conio.h>
    void main()
    {
    int n1,n2,n3;
    float sum,average;
    printf("enter 3 integer numbers\n");
    sum=(n1+n2+n3);
    average=sum/3;
    printf("The sum of 3 numbers is=%f\n,sum);
    printf=("The average of numbers=%f/n",average);
    getch()

    }





    out put
    please enter 3 integer numbers
    12
    25
    33
    sum of 3 numbers=70.000000
    avg of 3 numbers=23.333334

    Largest of 3 number


    /*Largest of 3 number */
    #include<stdio.h>
    #include<conio.h>
    void main()
    {
    int a,b,c;
    printf("enter the 3 numbers\n");
    scanf("%d %d %d",&a,&b,&c);
    if(a>b && a>c)
    printf("a is greater\n");
    else
    if(b>a && b>c)
    printf("b is greater");
    else
    printf("c is greater");

    getch();

    }




    out put
    enter the 3 numbers
    9
    7
    20
    c is greater

    To find whether a number is prime or not

    #include<stdio.h>
    #include<conio.h>
    main()
    {
       int i,number,remainder,interval;
       clrscr();
     /*program to test the prime property of a given number*/
     printf("type in the number to be tested\n");
     scanf("%d",&number);
     interval=number/2;
     for(i=2; i<=interval; ++i)
        {
        remainder=number%i;
        if(remainder==0)
        break;
        }
      if(remainder!=0)
        printf("given number %d is a PRIME NUMBER\n",number);
      else
        printf("given number %d is not a PRIME NUMBER\n",number);
      }


    OUTPUT

    type in the number to be tested
    43
    given number 43 is a PRIME NUMBER

    finding the roots of the quadratic equation using switch-statement



    #include<stdio.h>
    #include<conio.h>
    void main()
    {
    int option;
    float a,b,c,d;
    float root1,root2,r1,r2;
    clrscr();
    printf("enterthe value of a,b,c\n");
    scanf("%f%f%f",&a,&b,&c);
    if (a==0||b==0||c==0)
    {
    printf("\n error_we cannot analyse");
    exit();
    }
    d=(b*b-4*a*c);

    if(d>0)
     option=1;
    else

     if(d<0)
     option=2;
    else
     option=3;
    switch(option)
    {
    case1:
    printf("roots are real & distinct\n");
    root1=(-b+sqrt(d))/2*a;
    root2=(-b-sqrt(d))/2*a;
    printf("\n root1=%f root2=%f\n",root1,root2);
    break;

    case 2:
    printf("\n roots are imaginary & complex\n");
    r1=-b/2*a;
    r2=sqrt(abs(d))/2*a;
    printf("root1=%f+%f\n",r1,r2);

    case 3:
    printf("\n roots are real & equal\n");
    root1=root2=-b/2*a;
    printf("root1=%f\n,root2=%f\n",root1,root2);
    break;
    }
    getch();
    }



    OUTPUT

    enter the value of a,b,c
    22,33,44
     roots are imaginary & complex
    root1=-363.000000+27962.000000

    roots are real & equal
    root2=-363.000000

    whether number is even or odd


    /*whether number is even or odd*/
    #include<stdio.h>
    #include<conio.h>
    void main()
    {
    int num,remainder;
    clrscr();
    printf("enter the number\n");
    scanf("%d",&num);
    remainder=num%2;
    if (remainder==0)
    printf("the number is even\n");
    else
    printf("the number is odd\n");
    getch();
    }


    OUTPUT


    enter the number
    121
     the number is odd

    sum of digit of given number

    /*sum of digit of given number*/
    #include<stdio.h>
    #include<conio.h>
    void main()
    {
    int number,sum=0,r;
    clrscr();
    printf("enter the number\n");
    scanf("%d",&number);
    do
    {
    r=number%10;
    sum=sum+r;
    number=number/10;
    }
    while(number!=0);
    printf("sum of digit is=%d\n",sum);
    getch();
    }



    OUTPUT
    enter the number
    123
    sum of digit is=6
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