Code

#!/usr/bin/python3
# ====================================================================
# Galileo's - acceleration of gravity experiment
# --------------------------------------------------------------------
# roll a ball down a ramp. if you doubled the amount of time that
# the ball rolls, it travels four times as far.
# --------------------------------------------------------------------
# Note: the length of Galileo's ramp is input but ignored. it is only
# used to establish the slope of the ramp.
# --------------------------------------------------------------------
# From: https://www.maplesoft.com/support/help/maple/view.aspx?
#       path=MathApps%2FGalileosInclinedPlaneExperiment
# ====================================================================

import math
import numpy as np

# --------------------------------------------------------------------
# ---- freefall distance (falling in a gravity well)
# ---- g   acceleration of gravity
# ---- iv  initial velocity (+ is upwards;- is downwards)
# ---- t   time 
# --------------------------------------------------------------------

def freefall_distance(g,iv,t):
    d = (iv*t) -  ((g*t**2)/2.0)
    return d

# --------------------------------------------------------------------
# ---- distance traveled down Galileo's ramp
# ---- g   acceleration of gravity
# ---- h   height of Galileo's ramp
# ---- l   length of Galileo's ramp
# ---- t   time 
# --------------------------------------------------------------------

def ramp_distance(g,h,l,t):
    d = ((g*h)/(2*l)) * t**2
    return d

# --------------------------------------------------------------------
# ---- main
# --------------------------------------------------------------------

txt = '''
if you doubled the amount of time that the
ball rolls, it travels four times as far.'''
print(txt)

# ---- freefall

grav  = 32.0        # acceleration of gravity  (feet/sec/sec)
times = [1,2,3,4]   # list of times to test


# ---- freefall ------------------------------------------------------

print()
print('---- freefall distances ----------------')
print('time (sec) dist (ft)')
for t in times:
    d = freefall_distance(grav,0.0,t)
    print(f'{t:4}      {abs(d):9.1f}')

# ---- ramp distance (0 degrees) -------------------------------------
               
h = 32.0                # height of Galileo's ramp (feet)
l = 32.0                # length of Galileo's ramp (feet)

print()
print('---- ramp distance --(90 deg vertical)--')
print('time (sec) dist (ft)')
for t in times:
    d = ramp_distance(grav,h,l,t)
    print(f'{t:4}      {d:9.1f}')

# ---- ramp distance (45 degrees) ------------------------------------

deg = 45.0                         # ramp angle
h   = 16.0                         # height of Galileo's ramp (feet)
l   = h/math.sin(np.deg2rad(deg))  # length of Galileo's ramp (feet)

print()
print(f'---- ramp distance --({deg} deg)-----------')
print(f'ramp height={h:<0.1f} length={l:<7.1f}')
print('time (sec) dist (ft)')
for t in times:
    d = ramp_distance(grav,h,l,t)
    print(f'{t:4}      {d:9.1f}')

# ---- ramp distance (30 degrees) ------------------------------------

deg = 30.0                         # ramp angle
h   = 16.0                         # height of Galileo's ramp (feet)
l   = h/math.sin(np.deg2rad(deg))  # length of Galileo's ramp (feet)

print()
print(f'---- ramp distance --({deg} deg)-----------')
print(f'ramp height={h:<0.1f} length={l:<7.1f}')
print('time (sec) dist (ft)')
for t in times:
    d = ramp_distance(grav,h,l,t)
    print(f'{t:4}      {d:9.1f}')

# ---- ramp distance (10 degrees) ------------------------------------

deg = 10.0                         # ramp angle
h   = 16.0                         # height of Galileo's ramp (feet)
l   = h/math.sin(np.deg2rad(deg))  # length of Galileo's ramp (feet)

print()
print(f'---- ramp distance --({deg} deg)-----------')
print(f'ramp height={h:<0.1f} length={l:<7.1f}')
print('time (sec) dist (ft)')
for t in times:
    d = ramp_distance(grav,h,l,t)
    print(f'{t:4}      {d:9.1f}')

Output

if you doubled the amount of time that the
ball rolls, it travels four times as far.

---- freefall distances ----------------
time (sec) dist (ft)
   1           16.0
   2           64.0
   3          144.0
   4          256.0

---- ramp distance --(90 deg vertical)--
time (sec) dist (ft)
   1           16.0
   2           64.0
   3          144.0
   4          256.0

---- ramp distance --(45.0 deg)-----------
ramp height=16.0 length=22.6   
time (sec) dist (ft)
   1           11.3
   2           45.3
   3          101.8
   4          181.0

---- ramp distance --(30.0 deg)-----------
ramp height=16.0 length=32.0   
time (sec) dist (ft)
   1            8.0
   2           32.0
   3           72.0
   4          128.0

---- ramp distance --(10.0 deg)-----------
ramp height=16.0 length=92.1   
time (sec) dist (ft)
   1            2.8
   2           11.1
   3           25.0
   4           44.5