What Calculations Determine the Volleyball's Trajectory in Projectile Motion?

[Delta2]

I believe Haruspex's method does not require one to differentiate at all which I think is much nicer.

That's very true, I still like more your method for that exact reason, that it involves derivatives!

 

[haruspex]

Not sure what you mean here, but I agree if you correctly treat the system , you can solve one quadratic equation and some linear equations and get the angle and the velocities.

You get two linear equations in which the unknowns are v_y/v_x and 1/v_x², v_x and v_y being the initial velocity components.

 

[haruspex]

Ok, I can see Haruspex's method is the one to use (for sure).

It is no different from your own method in post #21. For some reason I had not seen that when I wrote post #23. There can be quite a delay.
I get two equations instead of three merely by taking coordinates relative to the launch point.

 

[verty]

It is no different from your own method in post #21. For some reason I had not seen that when I wrote post #23. There can be quite a delay.
I get two equations instead of three merely by taking coordinates relative to the launch point.

I meant working with the usual time formula. Solving those quadratics was not so difficult in this case.