# Launch Velocity for Simple 3D Projectile [duplicate]

This is a pretty easy question, but I can't quite figure out the answer. I have:

1. The initial position of a projectile.
2. The gravity vector.
3. The (stationary) target I want to hit.
4. A maximum launch speed of the projectile.

I want to calculate the initial velocity the projectile must be launched at to hit the target, assuming it follows a ballistic trajectory.

• My answer here (gamedev.stackexchange.com/questions/54732/…) provides the kinematic equations for motion under constant acceleration. This is adequate whenever your projectile never rises too far above the Earth's surface, so that gravity can be assumed constant. Dec 29, 2014 at 22:11
• Thank you, but these are the forward equations (i.e given v_0 and g, where will it be at time t?). Further, they are in only one dimension. What I need is a re-arrangement of these equations to infer v_0 from a target and g. Dec 29, 2014 at 22:30
• Ah, I see, I just needed to do a bit of algebra and I found it! Dec 29, 2014 at 22:38

Vector3 displacement = (end - start);