For loop to find roots

I am trying to find the roots of a function, with a parameter that changes. The function is that of a parabola

V=rand(10,1)

g=9.81

z0=500

I should use the following expression in for loop right?

t_roots=roots([-.5*g,V,z0])

Answer 1

[Askic V]

Yes, if V contains paramters, then the could would look like this:

V = rand(10,1);
g = 9.81;
z0 = 500;
for vi = 1: numel(V)
    t_roots = roots([-0.5*g,vi,z0])
end

t_roots = 2×1

10.1988 -9.9950

t_roots = 2×1

10.3023 -9.8946

t_roots = 2×1

10.4068 -9.7952

t_roots = 2×1

10.5124 -9.6969

t_roots = 2×1

10.6189 -9.5995

t_roots = 2×1

10.7265 -9.5033

t_roots = 2×1

10.8351 -9.4080

t_roots = 2×1

10.9448 -9.3138

t_roots = 2×1

11.0554 -9.2205

t_roots = 2×1

11.1671 -9.1283

[Giovanni Curiazio]

Thank a lot. Now if i want to plot the different parabolas , how i do that? I should put the x,y,x distances also in a loop?

[Askic V]

This is just a small example, but it should be sufficient to show you:

V = rand(3,1);
g = 9.81;
z0 = 500;
x = -12:0.1:12;
for vi = 1: numel(V)
    t_roots = roots([-0.5*g,vi,z0]);
    y = -0.5*g*x.^2+vi*x+z0;
    plot(x, y);
    hold on;
end

[Giovanni Curiazio]

OK, I should have explained myself better. Now I will put what I got , and I will try to explain better what I want to get

%% Parabola for 1 piece
g=9.80665; %agravity
z0= 14325; %starting height
x0=0;      
y0=0;
V_0=200*.3048; %starting velocity
gamma=0.78;
DeltaV_c=randn(10,3); %Speed increments in the three directions x, y, z

% Debris velocity components after the explosion
V_0x=V_0*cos(gamma)+DeltaV_c(1,1);
V_0y=0+DeltaV_c(1,2);
V_0z=V_0*sin(gamma)+DeltaV_c(1,3);

%debris flight time
t_radici=roots([-.5*g,V_0z,z0])

t_radici = 2×1

58.5698 -49.8805

t = linspace(0,t_radici(t_radici>0),1000);  

%distanza percorsa nelle tre direzioni
x=x0+V_0x*t;
y=y0+V_0y*t;
z=z0+V_0z*t-.5*g*t.^2;

figure(3);
plot3(x,y,z)
hold on
plot3(x0,y0,z0,'ro','MarkerSize',5)  
plot3(x(end),y(end),z(end),'ro','MarkerSize',5)
xlabel('Posizione x (m)')
ylabel('Posizione y (m)')
zlabel('Posizione z (m)')
grid on

%ground impact point
x_f=x(end)

x_f = 2.6214e+03

y_f=y(end)

y_f = 17.2835

z_f=z(end)

z_f = 0

[Giovanni Curiazio]

Now I would like to achieve the same thing but considering more debris: so the starting height remains the same but at the initial velocity I would like to add up all the elements of DeltaV_c (for each direction). And finally plot the different parabolas. In fact as you can see, in the code I used only the first line of DeltaV_c, now I would like to use all the lines so that I have 10 different speeds, so 10 parabolas

[Askic V]

I guess you are trying to achive something like this?

g=9.80665; %agravity
z0= 14325; %starting height
x0=0;      
y0=0;
V_0=200*.3048; %starting velocity
gamma=0.78;
DeltaV_c = randn(10,3); %Speed increments in the three directions x, y, z
% Debris velocity components after the explosion
[r,c] = size(DeltaV_c);
for i = 1:r % each row contains increments in directions
    V_0x=V_0*cos(gamma)+DeltaV_c(i,1);
    V_0y=0+DeltaV_c(i,2);
    V_0z=V_0*sin(gamma)+DeltaV_c(i,3);
    %debris flight time
    t_radici = roots([-.5*g,V_0z,z0]);
    
    t = linspace(0,t_radici(t_radici>0),1000);  
    %distanza percorsa nelle tre direzioni
    x=x0+V_0x*t;
    y=y0+V_0y*t;
    z=z0+V_0z*t-.5*g*t.^2;
    plot3(x,y,z)
    hold on
    plot3(x0,y0,z0,'ro','MarkerSize',5)  
    plot3(x(end),y(end),z(end),'ro','MarkerSize',5)
    xlabel('Posizione x (m)')
    ylabel('Posizione y (m)')
    zlabel('Posizione z (m)')
    grid on
end