Right now we are working on the projectile math needed to calculate the angle of our shooter. Our shooter is relatively similar to the Unqualfied Quokkas RI3D, with our shooter being placed on a rotating arm. This means that the distance required to shoot to the speaker will be dependent on the angle of our shot.
Given these constraints, how do we calculate the angle of our shooter required to hit the speaker?
Looking at the Wikipedia page for Projectile Motion, the equation to find the shooter angle given a static distance (x,y) is
{\displaystyle \theta =\arctan {\left({\frac {v^{2}\pm {\sqrt {v^{4}-g(gx^{2}+2yv^{2})}}}{gx}}\right)}}
The main difference with our problem is that the x distance and y distance are also functions of the angle, changing with the cosine and sine of the angle. Inputting this change into the function gives us approximately this equation where L is arm length
{\displaystyle \theta =\arctan {\left({\frac {v^{2}\pm {\sqrt {v^{4}-g(g(x + {L\cos(\theta))}^{2}+2(y - L\sin(\theta))v^{2})}}}{g(x + {L\cos(\theta)}))}}\right)}}
However, I have no idea where to begin to solve this equation. I don’t think it’s possible to solve, and there must be a better way to solve this. Does anyone have any ideas?