|V| - magnitude of the initial velocity vector Now, with this newest equation, we'll actually solve for vi_py and vi_pz. This gives us the initial velocity of the projectile along the y axis, in terms of vi_pz. We then plug in those values and solve for vi_py. Since we want to intercept the target, df_py equals df_ty. We know di_py is zero since we're centered at the origin. We have time t, the a_py may or may not be equal to a_ty, depending on the game engine, but I'll assume you know that value regardless. Vi_py : initial velocity - projectile's y component We'll be using a similar formula: df_py = a_py * t**2 / 2 + vi_py * t + di_pyĭf_py : final displacement - projectile's y componentĭi_py : initial displacement - projectile's y componentĪ_py : acceleration - projectile's y component With the df_ty value, we can now determine the initial y velocity of the projectile. We know t however (or, have an equation we can substitute in anyways), so we can plug in and solve for the final displacement (in terms of vi_pz). Vi_ty : initial velocity - target's y component Your target will follow a trajectory: df_ty = a_ty * t**2 / 2 + vi_ty * t + di_tyĭf_ty : final displacement - target's y componentĭi_ty : initial displacement - target's y componentĪ_ty : acceleration - target's y component Now, lets talk about your target's motion. t will be defined in terms of vi_pz, which is fine. We know df_pz is the distance to the target along the z-axis, and can solve for time t for the projectile to travel there. If we assume there's no air resistance, a_pz is zero, and since the origin is centered on you, di_pz is zero. Vi_pz : initial velocity - projectile's z component This gives us: df_pz = a_pz * t**2 / 2 + vi_pz * t + di_pzĭf_pz : final displacement - projectile's z componentĭi_pz : initial displacement - projectile's z componentĪ_pz : acceleration - projectile's z component Assuming there's no air drag, the projectile will move at a constant velocity along the z axis (it may accelerate along the y-axis, however).

We need to first talk about finding the time it takes a projectile to travel from you to the target. Orient your coordinate plane such that the y-axis is up/down from your perspective, and the z-axis passes through you and your target (+ being towards the target).

Projectile motion equation