#!/usr/bin/env python3
import math

g = 9.80665 # standard gravity (m/s^2)
p = 1.225   # density of 15°C air at sea level and (kg/m^3)

class Ball:
    def __init__(self, m, A, Cd):
        self.m = m      # mass (kg)
        self.A = A      # cross sectional area (m^2)
        self.Cd = Cd    # coefficient of drag
        self.z = 0      # distance fallen
        self.v = 0      # velocity
        self.p = p      # density of fluid
        self.g = g      # gravity
        self.vt = math.sqrt(2 * g * self.m / self.p / self.Cd / self.A)

    def drag(self, v):
        # 1/2 p Cd A v^2
        return 0.5 * self.p * self.Cd * self.A * v**2

    def step(self,dt):
        a = self.g - self.drag(self.v) / self.m
        self.z += self.v * dt + 0.5 * a * dt**2
        self.v += a * dt

    def reset(self):
        self.z = 0
        self.v = 0

def basketball(): return Ball(0.620, 0.750**2/4/math.pi, 0.47)
def bowling_ball(): return Ball(7.26, 0.6859**2/4/math.pi, 0.47)
def massive_sphere(r,m): return Ball(m, math.pi * r**2, 0.47)
def dense_sphere(r,d): return massive_sphere(r, d * 4 * math.pi * r**3 / 3)
def lead_sphere(r): return dense_sphere(r, 11340)
def pine_sphere(r): return dense_sphere(r, 500)
def pingpong_ball(): return Ball(0.0027, 0.02**2 * math.pi, 0.47)
def ant(): return Ball(0.000005, 0.00003, 0.8)
def rat(): return Ball(0.3, 0.04, 0.8)
def cat(): return Ball(4.0, 0.1, 0.8)
def person(): return Ball(70.0, 0.64, 0.6)
def phone(): return Ball(.174, .14*.07, 2.1)

def sim(balls):
    dt = 0.001
    for ms in range(10001):
        if ms % 100 == 0:
            out = [ms/1000]
            for b in balls:
                pt = 100 * b.v / b.vt
                out.append((round(b.z,2), round(b.v,2), round(pt,1)))
            print(out)
        for b in balls:
            b.step(dt)

balls = [phone(), ant(), rat(), cat(), person(), bowling_ball()]
sim(balls)
x = person()
print(x.vt)
x = phone()
print(x.vt)