it's been a while since I did any real math so I'm having a bit of a hard time with what should be a simple problem. I need to find an equation for intercepting a target (Item A) that's moving at a constant speed by throwing Item B at it from a fixed point. What I'm really interested in the angle at which I should throw Item B. (this is for a video game I'm making by the way)
I know the speed of Item A, I know the distance between Item A and B and I know that Item B will be thrown at a constant speed... I just need to figure out the angle (or the components x and y).
The way I went about it was by saying that the distance travelled by Item A at the moment of impact is:
Xa = Vax * t (Xa being the distance travelled and Vax its speed in x)
and the angle of Item B is :
cos th = adj / hip = Yb / (Vb * t)
substituting t we get :
Xa = Vax * Yb / (Vb * cos th)
Knowing that the distance in X between A and B is Xt = Xa + Xb :
Xt - Xb = Vax * Yb / (Vb * cos th)
Xt - Yb * tan th = Vax * Yb / (Vb * cos th)
Which finally gives :
Xt * cos th - Yb * sin th = Vax * Yb / Vb
The only thing unknown in this equation is the angle th... any help on how I could solve this, and eventually any corrections on the procedure?