Obtain value of a variable when y = 0 in a function

Im going trought matlab intro in college and got this project that is making me crazy.

The X and Y equations listed below on the code represent the X and Y components of coordinate pairs that simulate the position at an specific time while an object is going through parabolic motion. I must generate various (X,Y) components that plot the trayectory with the inputed constants whom will satisfy such functions. My problem is that I do not know to make this code stop plotting when it "reaches the ground" (X,0) and calculate the time it takes to do that (time is represented by "i" in the X and Y equation). The only way that I got the program to plot something was by generating a loop that placed an iteration limit (represented by "u" on the code); I have not been able to obtain the "i" value when the coordinate (X,0) is generated.

Thanks for taking the time to help me, I look foward to learn more and more about this topics.

clear 
clc
%Data inputs
fprintf('parabolic motion 1\n');
fprintf(1,'Provide an entry for the following constants\n');
V0 = input('Initial velocity = ');
b0 = input('Theta =  ');
C = input('"C" = Proyectile mass / air resistance coefficient =  ');
u = input('Number of desired plotted points =  ');
vy = V0*cosd(b0)
vx = V0*sind(b0)
x=0
y=0
i=1

     while (i <= u)
        %X and Y equations that make up the coordinate pair
        x(i) = C * vx * (1-2.718^(-(i)/C));
        y(i) = (C * vy + 9.8 * ((C)^2))*(1-2.718^(-(i)/C))-9.8 * C * (i);
        
        disp(x)
        disp(y)
        
        i = i+1 ;
        
    end 
figure
plot(x,y)
grid
xlabel('Distance (m)')
ylabel('Altitude (m)')

Answer 1

[Star Strider]

One option is to add a test for the value of ‘y’ as I did here.

V0 = 420;
b0 = 60;
C = pi;
u = 50;

%Data inputs
fprintf('parabolic motion 1\n');

parabolic motion 1

fprintf(1,'Provide an entry for the following constants\n');

Provide an entry for the following constants

% V0 = input('Initial velocity = ');
% b0 = input('Theta =  ');
% C = input('"C" = Proyectile mass / air resistance coefficient =  ');
% u = input('Number of desired plotted points =  ');
vy = V0*cosd(b0)

vy = 210

vx = V0*sind(b0)

vx = 363.7307

x=0

x = 0

y=0

y = 0

i=1

i = 1

     while (i <= u) & all(y >= 0) 
        %X and Y equations that make up the coordinate pair
        x(i) = C * vx * (1-2.718^(-(i)/C));
        y(i) = (C * vy + 9.8 * ((C)^2))*(1-2.718^(-(i)/C))-9.8 * C * (i);
        
        disp(x)
        disp(y)
        
        i = i+1 ;
        
    end 

  311.4967

  175.4214

  311.4967  538.0799

  175.4214  294.6306

  311.4967  538.0799  702.8968

  175.4214  294.6306  372.9508

  311.4967  538.0799  702.8968  822.7848

  175.4214  294.6306  372.9508  421.5283

  311.4967  538.0799  702.8968  822.7848  909.9915

  175.4214  294.6306  372.9508  421.5283  448.4711

  311.4967  538.0799  702.8968  822.7848  909.9915  973.4258

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407    1.1413

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035  108.9705

   1.0e+03 *

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407    1.1413    1.1417

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035  108.9705   78.4408

   1.0e+03 *

  Columns 1 through 22

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407    1.1413    1.1417

  Column 23

    1.1419

  Columns 1 through 22

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035  108.9705   78.4408

  Column 23

   47.8409

   1.0e+03 *

  Columns 1 through 22

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407    1.1413    1.1417

  Columns 23 through 24

    1.1419    1.1421

  Columns 1 through 22

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035  108.9705   78.4408

  Columns 23 through 24

   47.8409   17.1898

   1.0e+03 *

  Columns 1 through 22

    0.3115    0.5381    0.7029    0.8228    0.9100    0.9734    1.0196    1.0531    1.0775    1.0953    1.1082    1.1176    1.1245    1.1294    1.1330    1.1357    1.1376    1.1390    1.1400    1.1407    1.1413    1.1417

  Columns 23 through 25

    1.1419    1.1421    1.1423

  Columns 1 through 22

  175.4214  294.6306  372.9508  421.5283  448.4711  459.6766  459.4349  450.8663  436.2409  417.2097  394.9738  370.4066  344.1438  316.6475  288.2540  259.2079  229.6870  199.8209  169.7035  139.4035  108.9705   78.4408

  Columns 23 through 25

   47.8409   17.1898  -13.4986

figure
plot(x,y)
grid
xlabel('Distance (m)')
ylabel('Altitude (m)')

Since the ‘y’ test only stops when the first value of ‘y’ is negative, one option is to plot only ‘t(1:end-1)’ and ‘y(1:end-1)’ so ‘y’ always remains positive on the plot (even though using that approach it may never actually reach 0 and so is left floating above the ground for all eternity as the result).

.