Rotate arrow without unity physics engine.

I have this code that simulates the movement of a projectile without using the unity physics engine

 IEnumerator LaunchProjectile(int angle, float speed)
 {
     
     // Move projectile to the position of throwing object + add some offset if needed.
     Projectile.position = transform.position + new Vector3(0, 0f, 0);
     Projectile.rotation = transform.root.rotation;
     Debug.Log(transform.root.eulerAngles);
     
     // Calculate distance to target
     float target_Distance = speed * (Mathf.Sin(2 * firingAngle * Mathf.Deg2Rad) / gravity);
     
     // Extract the X  Y componenent of the velocity
     float Vx = Mathf.Sqrt(speed) * Mathf.Cos(firingAngle * Mathf.Deg2Rad);
     float Vy = Mathf.Sqrt(speed) * Mathf.Sin(firingAngle * Mathf.Deg2Rad); 
     
     // Calculate flight time.
     float flightDuration = target_Distance / Vx;
     
     // Rotate projectile to face the target.
     //Projectile.rotation = Quaternion.LookRotation(Target.position - Projectile.position);
     
     this.arrowSimulationScript = Projectile.gameObject.GetComponentInChildren<ArrowSimulation>();
     
     float elapse_time = 0;

     while (!arrowSimulationScript.Collided())
     {
         Projectile.Translate(0, (Vy - (gravity * elapse_time)) * Time.deltaTime, Vx * Time.deltaTime);

         Projectile.LookAt(Projectile.position - new Vector3(0,  (Vy - (gravity * elapse_time)) * Time.deltaTime, Vx * Time.deltaTime));

         arrowSimulationScript.Velocity = new Vector3(0, (Vy - (gravity * elapse_time)) * Time.deltaTime, Vx * Time.deltaTime).magnitude;
         
         elapse_time += Time.deltaTime;
         
         yield return null;
     }
 }

The arrow is fired in the direction of the object which has this script attached. To make the arrow rotate I use this line of code:

 Projectile.LookAt(Projectile.position - new Vector3(0,  (Vy - (gravity * elapse_time)) * Time.deltaTime, Vx * Time.deltaTime));

The arrow moves towards the right direction but with the tip facing the z axis direction, instead of the direction of the bow. Here is a video of the problem: https://www.youtube.com/watch?v=cyK6DXxTw_E

If I comment out that line of code the arrow fly with the tip facing the direction of the bow, but it doesn't rotate.