public class BallLauncher : MonoBehaviour {

public Rigidbody ball;
public Transform target;

public float h = 25;
public float gravity = -18;

public bool debugPath;

void Start() {
    ball.useGravity = false;
}

void Update() {
    if (Input.GetKeyDown (KeyCode.Space)) {
        Launch ();
    }

    if (debugPath) {
        DrawPath ();
    }
}

void Launch() {
    Physics.gravity = Vector3.up * gravity;
    ball.useGravity = true;
    ball.velocity = CalculateLaunchData ().initialVelocity;
}

LaunchData CalculateLaunchData() {
    float displacementY = target.position.y - ball.position.y;
    Vector3 displacementXZ = new Vector3 (target.position.x - ball.position.x, 0, target.position.z - ball.position.z);
    float time = Mathf.Sqrt(-2*h/gravity) + Mathf.Sqrt(2*(displacementY - h)/gravity);
    Vector3 velocityY = Vector3.up * Mathf.Sqrt (-2 * gravity * h);
    Vector3 velocityXZ = displacementXZ / time;

    return new LaunchData(velocityXZ + velocityY * -Mathf.Sign(gravity), time);
}

void DrawPath() {
    LaunchData launchData = CalculateLaunchData ();
    Vector3 previousDrawPoint = ball.position;

    int resolution = 30;
    for (int i = 1; i <= resolution; i++) {
        float simulationTime = i / (float)resolution * launchData.timeToTarget;
        Vector3 displacement = launchData.initialVelocity * simulationTime + Vector3.up *gravity * simulationTime * simulationTime / 2f;
        Vector3 drawPoint = ball.position + displacement;
        Debug.DrawLine (previousDrawPoint, drawPoint, Color.green);
        previousDrawPoint = drawPoint;
    }
}

struct LaunchData {
    public readonly Vector3 initialVelocity;
    public readonly float timeToTarget;

    public LaunchData (Vector3 initialVelocity, float timeToTarget)
    {
        this.initialVelocity = initialVelocity;
        this.timeToTarget = timeToTarget;
    }

}