Please help solve and plot the solutions to an equation

I have an equation:

D2=(((V2)^2*(sind(2*A2)))/(2*g))*(1+(1+((2*g*H2)/((V2)^2*(sind(A2))^2)))^0.5)

which represents the distance jumped based on height, starting speed, etc etc.

I know the distance jumped D2=11.4m, the height, H2=25.2m, and g=9.81

Assuming A2 can be angles ranging from 0 to 90, I would like to work out possible values of V2(starting speed) matching these angles.

The idea is to plot the values of V2 corresponding to each angle.

Any ideas how I could solve and plot this?

Thank you in advance for the help!

Answer 1

[Divija Aleti]

Hi Alexander,

Have a look at the following code. It shows one of the ways by which you can solve your question.

D2 = 11.4;
H2 = 25.2;
g = 9.81;
A2 = 1:1:89;
V = zeros([89 1]);
syms V2
for i = 1:89
    eqn = D2-(((V2)^2*(sind(2*A2(i))))/(2*g))*(1+(1+((2*g*H2)/((V2)^2*(sind(A2(i)))^2)))^0.5)==0;
    S = solve(eqn,V2);
    if S(1)>=0
        V(i) = S(1);
    else
        V(i) = S(2);
    end
end
plot(A2,V)

Output:

For each value of A2, two values of V2 are obtained, out of which I have selected the positive values for plotting. You can also select the negative values.

For additional information on the 'solve' function, refer to the following link :

Equations and systems solver - MATLAB solve (mathworks.com)

Regards,

Divija

[Alexander Jacobs]

Thank you so, so much, Divija. That really helps! Thanks again