Move object to Vector3 position with keeping gravity

I have such a problem, maybe someone will help. I am making a game and I need to make a dice that goes in the direction opposite to the click. For example, clicking on the back of a cube moves it forward, etc. Gravity must act on the cube as shown in the figure below. Unfortunately, the cube does not change height, but only the position of X and Z. Please help.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class MoveCube : MonoBehaviour
{
Vector3 movePosition;
public float time = 0.02f;

[HideInInspector]
public bool blockClick = false;

private void Start()
{
    movePosition = transform.position;
}

private void Update()
{
    blockClick = false;

    if (Input.GetMouseButtonDown(0))
    {
        Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
        RaycastHit raycastHit;

        if (Physics.Raycast(ray, out raycastHit))
        {
            string hitName = raycastHit.transform.name;

            if (hitName == "MoveCube")
            {
                move(raycastHit);
                blockClick = true;
            }
        }
    }

    transform.position = Vector3.Lerp(
            transform.position,
            movePosition,
            time);
}

public void move(RaycastHit raycastHit)
{
    Vector3 incomingVec = raycastHit.normal - Vector3.up;

    // South
    if (incomingVec == new Vector3(0, -1, -1))
    {
        movePosition = movePosition + new Vector3(0, 0, 1);
        return;
    }

    // North
    if (incomingVec == new Vector3(0, -1, 1))
    {
        movePosition = movePosition + new Vector3(0, 0, -1);
        return;
    }

    // West
    if (incomingVec == new Vector3(-1, -1, 0))
    {
        movePosition = movePosition + new Vector3(1, 0, 0);
        return;
    }

    // East
    if (incomingVec == new Vector3(1, -1, 0))
    {
        movePosition = movePosition + new Vector3(-1, 0, 0);
        return;
    }
}
}