How to predict where the ball will fall?

For my examples, I'll be reusing a little content I previously included here.

Because you already have the velocity of the ball at any given time, you can create a prediction of where the ball will be by stepping through Unity's general physics steps.

To note, the general implementations of drag and velocity (per physics update) in Unity are:

 rigidbodyDrag = Mathf.Clamp01(1.0f - (rb.drag * Time.fixedDeltaTime)); // Per FixedUpdate()
 // This means that if your drag is equal to the framerate of FixedUpdate(), your object will lose 100% of its speed every frame
 
 velocityPerFrame = lastFrameVelocity + (Physics.gravity * Time.fixedDeltaTime);
 velocityPerFrame *= rigidbodyDrag;
 positionPerFrame += (velocityPerFrame * Time.fixedDeltaTime);

With those taken into consideration, you'll want to create either a list or an array (with a maximum time estimate factored in as a safety), then populate it (at least) until your goal is met.

 // C#
 // Example maximum of 5 seconds
 int maxIterations = Mathf.RoundToInt(5.0f / Time.fixedDeltaTime);
 Vector3 pos = ball.position;
 Vector3 vel = ballRigidbody.velocity;
 float drag = Mathf.Clamp01(1.0f - (ballRigidbody.drag * Time.fixedDeltaTime));
 positionList.Add(pos);
 float elapsedTime = 0.0f;
 
 for(int i = 0; i < maxIterations; i++)
 {
     vel = vel + (Physics.gravity * Time.fixedDeltaTime)
     vel *= drag;
     pos += vel * Time.fixedDeltaTime;
     elapsedTime += Time.fixedDeltaTime;
     positionList.Add(pos);
     if(pos.y - ballRadius < targetHeight && Vector3.Dot(vel, Vector3.down) > 0)
     {
         // The ball must be moving downward to fit the second criteria
         break;
     }
 }

Using this approach, the prediction would only need to be updated when something directly modifies the ball's current trajectory (or if the ball was rocketing into space and would take longer to return than the safety timeout).

^{Edit: Added in time factor}

You will have to record the velocity at which the ball is shot - taking into consideration the z component you can calculate the time it will be in the air. Since you have the time and the x component of the shot, you only need to multiply the time with the x component of the ball's velocity to find out at what distance the ball is going to be from the position it was shot at. Finally, by looking at the x and y component of the velocity, you can create a Vector2 that will give you the direction of the shot. You will need to normalize the Vector2 and multiply it by the distance, and that will give you a Vector2 from the position the ball was shot to the position the ball is going to land. Once you have that Vector2, just add the original position the ball was shot from to it, and you'll get the X and Y coordinates of the place your AI has to go to.

This is all fine and dandy, but honestly it would be way better if you just made your AI follow the X and Y coordinates of the ball, and if they can make it to the ball, cool, if not, well, a real player couldn't either. While it's precise to define an AI to get the ball, it is more realistic to make it follow the X and Y position of the ball like a real player would, although most pro basketball players have enough experience to make a good judgement on where the ball will fall anyways.

tl;dr you can use the x and y components of an angled shot from physics to calculate the time, the distance and the location of the point the ball will fall, or you could simply make your AI move with a velocity Vector3 equal to (ballposition.x - AIposition.x, ballposition.y - AIposition.y, AIposition.z).normalized times an arbitrary constant.

I am creating a 3D basketball game also. Need answers too. Best answer for rebounding is Using 'Colliders as Triggers' https://www.youtube.com/watch?v=BYwkd80T5Zk https://unity3d.com/learn/tutorials/topics/physics/colliders-triggers In theory, one or invisible 'colliders' near backboard/rim space and invisible 'colliders' in key areas under basket where player rebounding most likely to happen. Two events, basketball in collider space triggers nearest player animation in rebounding collider space. In code calculate for speed, velocity, trajectory as in relation to collider triggers.

Hello! Sorry ... I'd need something similar but on a 2D knowing where the ball is going to fall on the X axsis... in a ArcadeVolleyball like game!