MATLAB: Find x for y=0 using interpolation

Question

Hello there,

I was given the task to find the x value where y is 0 using interpolation. And I just can not figure it out on my own.

First of all: Here is my complete code:

load Daten_Wurfparabel.mat
h_index = find(y<0,1)           ;
index   = [ h_index-1 h_index]  ;
xx      = x(index)              ;
yy      = y(index)              ;
x0      = xx(1)+1               ;
y0      = 0                     ;
w       = interp1( x , y , xx ) ;
% Plot
figure (1), clf
subplot(2,1,1)
    hold on , grid on
    plot(x ,y ,'ko-')
    plot(xx,yy,'r*','markersize',10)
    xlabel('x [m]'), ylabel('y [m]')
    title('Wurfparabel y über x')
subplot(2,1,2)
    hold on , grid on
    plot(xx ,yy ,'ko-')
    plot(xx,yy,'r*','markersize',10)
    plot(x0, y0, 'ko')
    xlim([19 21]), ylim([-0.5 1])
    xlabel('x [m]'), ylabel('y [m]')
    title('Vergrößerung des Nulldurchgangs')
    
% Ausgabe im CW
disp('Wurfweite [m] = x-Wert bei Nulldurchgang y = 0')
    disp(x0(1))

As you can see. I'm loading data from a .mat file (x is a 21×1 matrix and y is a 21×1 matrix). I have attached the file below. If you paste my code into matlab, you can see that I'm off by a few centimeters. The solution should be 20.2479m and mine is currently 20.3990m.

Can someone please help me out?

Answer 1

load ("Daten_Wurfparabel.mat") ; 
yi = 0 ; 
xi = interp1(y,x,0) ; 
[xi yi]
plot(x,y,'b')
hold on
plot(xi,yi,'*r')