(* auto eval 4.2 *)


(* 1. *)
type t_point_vector = {x : float; y : float};; (* type vector & type
point didn't has any difference *)
type t_ball = {pos : t_point_vector; speed : t_point_vector};;

(* 2. *)

let gravity : t_point_vector = {x = 0.; y = -9.80665};;


(* 3. *)

let sum_vector(vector_1, vector_2 : t_point_vector * t_point_vector) :
t_point_vector =
   {x = vector_1.x +. vector_2.x; y = vector_1.y +. vector_2.y}
;;

let init_ball(height, speed : float * t_point_vector) : t_ball =
  let init_point : t_point_vector = {x = 0.; y = height} in {pos =
init_point; speed = speed}
;;

let rec compute_next_speed(ball, t : t_ball * int) : t_point_vector =
  if t = 0
  then ball.speed
  else
    sum_vector(compute_next_speed(ball, t-1), gravity)
;;

(* 4. *)

let rec compute_next_pos(ball , t: t_ball * int) : t_point_vector =
  if t = 0
  then ball.pos
  else
    let speed : t_point_vector = compute_next_speed(ball, t-1) in
    sum_vector(compute_next_pos(ball, t-1), {x = speed.x; y = speed.y})
;;

(* 5. *)

let rec compute_end_point(ball, t : t_ball * int) : t_point_vector =
  let pos : t_point_vector = compute_next_pos(ball, t) in
  if pos.y < 0.
  then compute_next_pos(ball, t)
  else
    compute_end_point(ball, t+1)
;;

compute_end_point({pos = {x = 0.; y = 1000.}; speed = {x = 0.; y = 0.}}, 10);;