I am working making a soccer game in a game engine and encountered a problem with calculating what velocity a ball has to be kicked in to get from A to B.
the ball has to be passed (on a flat surface with friction coefficient of 0.35) from point A to point B, but since this is a 3d world the ball's velocity will be over 2 axes (the z axis velocity will always be 0).
distance between point A to point B is known and so is the required travel time.
this means i should be able to find the required initial velocity to get from A to B using :
Vi = (displacement / time) - (0.5 * acceleration * time);
but i must use this formula separately for each of the 2 axes (x and y), and the acceleration value seems to be different for each of these axes.
to calculate the acceleration (or rather deceleration) i found that i can use gravity * friction coefficient), but the value i get needs to somehow be distributed over the 2 axes in which movement occurs.
I was able to run the simulation and have the ball roll along the surface, and by comparing its velocities over time i was able to deduct that the acceleration being applied to it has a vector length which equals gravity * friction coefficient; But i am unsure on how to calculate the acceleration per axis.
The Attempt at a Solution
I've tried looking up all relevant formulas, which initially lead me to try and having a physically accurate ball movement in my simulation, and further research (or rather, debugging) lead me to find that my actual problem was not thinking about these formulas in 3d terms