This weeks exercise is based on problem 417 in your MATLAB b

This week\'s exercise is based on problem 4.17 in your MATLAB book^1. The airplane shown is flying in a circular path with radius rho, the bottom of which is located at a height h above the ground, with constant tangential velocity nu. The airplane\'s position is being tracked by radar station on the ground. In this exercise, you will be calculating the airplane\'s radial distance r and elevation theta relative to the radar station. Start MATLAB, navigate to the directory where you want to save your work, and start a new m-file called \"W10.m\". Your program should do the following: PART 1: using the \'input\' command, prompt the user for nu, rho, and h. (When testing your code, try using the values nu = 50 m/s, rho = 2000m, and h = 500m as shown in your book). PART 2: using the \'linspace\' command, create a 100-element time vector going from zero to the time at which infinity = 90 degree. To calculate the upper time limit, calculate the circumferential distance traveled between infinity = 0 degree and infinity = 90 degree, then divide by tangential velocity to get time. PART 3: create a vector for a as a function of time, using the following relationship: alpha(t) = nu/rho t PART 4: create vectors that represent the horizontal and vertical (x, y) coordinates of the airplane relative to the radar station, using the following equations: x(alpha) = rho sin alpha y(alpha) = rho(1 - cos alpha) + h PART 5: convert your rectangular (x, y) coordinates into polar (r, theta) coordinates. PART 6: using the \'min\' command, determine the minimum value of theta, and the position in the theta vector where the minimum occurs. Use the latter as an array index to find the values of t and r where theta is minimized. PART 7: using the \'fprintf\' command, display a message in the command window that includes the minimal value of theta, as well as the t and r values where the minimum occurs. PART 8: combine your t, r, and theta vectors intoTsingle 3 times 100 matrix variable called voutput. Then, write this matrix to an output file using the following steps: a. Use the \'fopen\'command to create a new file called \'output.doc\'. b. Use the \'fprintf\' command to write the column headers \'TIME\', \'DISTANCE\', and \'ANGLE\' to your output.doc file c. Use the \'fprintf\' command to write your voutput matrix to the output.doc file d. Use the \'fclose\' command to close your output file. When finished, upload BOTH files (W10.m AND output.doc) to Blackboard using the link provided. REFERENCE Gilat A., MATLAB: An Introduction with Applications, 4^th ed., Wiley, Hoboken, NJ, 2011.

The following is the required MATLAB function:

function w10

clc % Clears the command window screen

v=input(\'enter the value for v \ \');

Rho=input(\'enter the value for Rho \ \');

h=input(\'enter the value for h \ \');

t=Rho*pi/2/v;

fprintf(\'\ The time at which alpha is 90 deg is %f \',t)

i=1;

fprintf(\'\ Rho Velocity h\')

fprintf(\'\ %3.3f\\t\\t%3.3f\\t\\t%3.3f\',Rho,v,h)

fprintf(\'\ \ \ \')

disp(\'Time(t) Theta(radians) Radius(m)\')

for x=linspace(0,t)

t(i)=x;

Alpha(i)=(v*t(i))/Rho;

x(i)=Rho*sin(Alpha(i));

y(i)=Rho*(1-cos(Alpha(i)))+h;

[Theta(i),r(i)]=cart2pol(x(i),y(i));

fprintf(\'\ %3.3f\\t\\t%3.3f\\t\\t%3.3f\',t(i),Theta(i),r(i))

i=i+1;

end

[Tmin,I]=min(Theta);

fprintf(\'\ The minimum value of Theta and the values of t and r corresponding to Theta minimum are \ %3.3f\\t%3.3f\\t%3.3f\ \',Tmin,t(I),r(I));

end

Save the file with .m extension and recall the function in command work space.

The following is the output:

enter the value for v

enter the value for Rho

2000

enter the value for h

500

The time at which alpha is 90 deg is 62.831853

Rho Velocity h

2000.000 50.000 500.000

Time(t) Theta(radians) Radius(m)

0.000 1.571 500.000

0.635 1.507 501.257

1.269 1.445 505.009

1.904 1.384 511.201

2.539 1.324 519.743

3.173 1.267 530.521

3.808 1.213 543.397

4.443 1.162 558.225

5.077 1.115 574.849

5.712 1.070 593.115

6.347 1.029 612.871

6.981 0.991 633.974

7.616 0.956 656.287

8.251 0.924 679.688

8.885 0.895 704.061

9.520 0.868 729.304

10.155 0.843 755.323

10.789 0.821 782.035

11.424 0.801 809.364

12.059 0.782 837.244

12.693 0.766 865.615

13.328 0.750 894.423

13.963 0.737 923.620

14.597 0.724 953.164

15.232 0.713 983.016

15.867 0.703 1013.142

16.501 0.694 1043.511

17.136 0.686 1074.095

17.771 0.679 1104.869

18.405 0.673 1135.809

19.040 0.667 1166.896

19.675 0.663 1198.109

20.309 0.658 1229.433

20.944 0.655 1260.851

21.579 0.652 1292.349

22.213 0.649 1323.913

22.848 0.647 1355.531

23.483 0.646 1387.192

24.117 0.645 1418.885

24.752 0.644 1450.600

25.387 0.644 1482.328

26.021 0.644 1514.061

26.656 0.644 1545.791

27.291 0.644 1577.509

27.925 0.645 1609.210

28.560 0.647 1640.885

29.195 0.648 1672.530

29.829 0.650 1704.137

30.464 0.652 1735.701

31.099 0.654 1767.218

31.733 0.656 1798.680

32.368 0.658 1830.085

33.003 0.661 1861.426

33.637 0.664 1892.699

34.272 0.667 1923.900

34.907 0.670 1955.025

35.541 0.674 1986.070

36.176 0.677 2017.030

36.811 0.681 2047.902

37.445 0.684 2078.682

38.080 0.688 2109.367

38.715 0.692 2139.954

39.349 0.696 2170.438

39.984 0.701 2200.816

40.619 0.705 2231.086

41.253 0.709 2261.244

41.888 0.714 2291.288

42.523 0.718 2321.214

43.157 0.723 2351.019

43.792 0.728 2380.700

44.427 0.733 2410.256

45.061 0.737 2439.683

45.696 0.742 2468.977

46.331 0.747 2498.138

46.965 0.753 2527.162

47.600 0.758 2556.047

48.235 0.763 2584.790

48.869 0.768 2613.388

49.504 0.774 2641.840

50.139 0.779 2670.143

50.773 0.784 2698.295

51.408 0.790 2726.293

52.043 0.796 2754.135

52.677 0.801 2781.820

53.312 0.807 2809.343

53.947 0.812 2836.705

54.581 0.818 2863.902

55.216 0.824 2890.932

55.851 0.830 2917.793

56.485 0.836 2944.484

57.120 0.842 2971.002

57.755 0.847 2997.345

58.389 0.853 3023.511

59.024 0.859 3049.498

59.659 0.865 3075.305

60.293 0.872 3100.929

60.928 0.878 3126.369

61.563 0.884 3151.622

62.197 0.890 3176.687

62.832 0.896 3201.562

The minimum value of Theta and the values of t and r corresponding to Theta minimum are

0.644 26.021 1514.061

$This week\'s exercise is based on problem 4.17 in your MATLAB book^1. The airplane shown is flying in a circular path with radius rho, the bottom of which is l$

This weeks exercise is based on problem 417 in your MATLAB b

Solution

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