#----------------------------------------------------------------------
# Copyright (C) April 24, 2017 -- Dr. William T. Verts
#
# In the movie "The Avengers" (2012) there is a scene where Tony Stark
# (Iron Man) faces off with Loki in Stark Tower.  Eventually, Loki
# throws Tony out a window, but Tony's Iron Man armor flies out,
# catches up, envelopes him, powers up, and activates before he hits
# the ground.  From the timing, and basic physics (omitting such things
# as air resistance), how tall is Stark Tower at minimum?  (We don't
# know anything about the building height above the current floor.)
#
# https://www.youtube.com/watch?v=65XnYhk785s
#
# In the video, Loki tosses Tony out the window at 3:07, and Tony fires
# his repulsors to stop his fall just before hitting the ground at
# 3:31.  He falls for 24 seconds.
#
# What do we need to know?
# (1) Acceleration due to gravity (around 9.8 meters/second-squared)
# (2) Basic distance-acceleration-time formula: D = (1/2) A T^2
#
# Here is a quick-and-dirty attempt, knowing that we will eventually
# need to replace GetATime with a better routine to accept times as
# minutes:seconds.
#----------------------------------------------------------------------

def GetATime1 (Message):
    return requestInteger(Message)
    
def Main1 ():
    Start = GetATime1("Enter Start Time")
    Stop  = GetATime1("Enter Stop Time")
    Elapsed = Stop - Start
    Acceleration = 9.8
    Distance = 0.5 * Acceleration * Elapsed * Elapsed
    print "Distance = ", Distance, " meters"
    return

#----------------------------------------------------------------------
# Now, that program may be fine to get a quick answer (2822.4 meters),
# but (A) it is not very general, and (B) it doesn't protect against
# stupid data entry errors.
#
# Here is a better version where GetATime can now detect a colon and
# from that figure out the minutes and seconds if one is present, or
# figure out just seconds if there is no colon.  Also, it protects
# against the user entering something that is not a correctly formatted
# time, and loops until it gets something acceptable.  The try-except
# structure detects errors that would break the program and lets the
# program continue.
#
# We also introduce a new function to compute the acceleration due
# to gravity based on latitude, because the acceleration is different
# at the poles from at the equator and at 45 degrees latitude.  The
# GetAcceleration function computes a tighter value.  (New York City,
# where Stark Tower is located, is at latitude 40.7128 north.)
#
# Finally, we compute the distance in both feet and meters.
#
# Our final program can now handle a wide variety of input values.
# We can correct for latitude, we can enter times as seconds or as
# minutes:seconds, and illegal values are detected and programmed
# around.
#
# Note that the answers, 2823 meters / 9262 feet are completely
# unreasonable for the heights of buildings.  First, the tallest
# building in the world is only (!) 830 meters / 2722 feet tall,
# making Stark Tower taller by a factor of 3.4:1, and nearly two miles
# tall.  We can tell from the video that this is ridiculous, as there
# is a level shot of the Chrysler Building out the window of Stark
# Tower; the Chrysler Building is 319 meters / 1046 feet tall.
# Hollywood has taken liberties with physics once again!
#----------------------------------------------------------------------

import string

def GetATime2 (Message):
    Result = -1                         # Force loop to run at least once
    while Result < 0:
        try:
            S = requestString(Message)  # Ask the user for the time
            N = string.find(S, ":")     # Value is 0...len(S)-1 if found, -1 if not found
            if N >= 0:                  # The colon is present
                Prefix = S[:N]          #     Pick off string left of colon
                Suffix = S[N+1:]        #     Pick off string right of colon
                Minutes = int(Prefix)   #     Attempt to convert, throw error if illegal
                Seconds = int(Suffix)   #     Attempt to convert, throw error if illegal
            else:                       # The colon is not present
                Minutes = 0             #     No minutes, use entire string as seconds
                Seconds = int(S)        #     Attempt to convert, throw error if illegal
            Result = Minutes * 60 + Seconds
        except:
            Result = -1                 # Catch any errors, force loop to run once more
    return Result
        
def GetAcceleration (Latitude):   # Latitude is in Degrees
    AccelPoles   = 9.832
    Accel45      = 9.806
    AccelEquator = 9.780
    return Accel45 - 0.5 * (AccelPoles - AccelEquator) * cos(2.0*Latitude*pi/180.0)
    
def Main2():
    FeetPerMeter = 3.28084
    Acceleration = GetAcceleration(requestNumber("Enter Latitude"))
    Start = GetATime2("Enter Starting Time")
    Stop  = GetATime2("Enter Ending Time")
    Elapsed = Stop - Start
    DistanceMeters = 0.5 * Acceleration * Elapsed * Elapsed
    DistanceFeet  = DistanceMeters * FeetPerMeter
    print "Height in meters = ", DistanceMeters
    print "Height in feet = ", DistanceFeet
    return
    
#----------------------------------------------------------------------
# Notice that the code to be more general and more forgiving of data
# entry problems is quite a bit longer than the version that assumes
# the user will behave and enter values correctly.  This is pretty
# typical.  It always takes more time and more code to idiot-proof a
# program.
#----------------------------------------------------------------------