Math problem #1a (plus a little science): In Chicago ["http://www.timeanddate.com/worldclock/astronomy.html?n=64"], the earliest possible sunset time ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=12&year=2009&obj=sun&afl=-11&day=1"] is 4:20 p.m., and the earliest sunrise time ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=6&year=2009&obj=sun&afl=-11&day=1"] 5:15 a.m. (4:15 a.m. after subtracting an hour due to Daylight Saving Time); the latest sunset time ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=6&year=2009&obj=sun&afl=-11&day=1"] is 8:30 p.m. (7:30 p.m. after subtracting from DST), and the latest sunrise time ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=1&year=2010&obj=sun&afl=-11&day=1"] is 7:18 a.m. The problem (yes, this is a literal problem in my opinion): after finding the difference between the earliest and latest possible sunrise times, and the earliest and latest sunset times (make sure to convert the earliest sunrise and latest sunset times to non-DST), it turns out that the change between earliest and latest sunset times is seven minutes greater (3h 10m) than the corresponding sunrise times (3h 3m).
Math problem #1b: According to timeanddate.com ["http://timeanddate.com/"], the sunrise and sunset times on June 21, 2009 (the summer solstice) ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=6&year=2009&obj=sun&afl=-11&day=1"] are 5:16 a.m. and 8:29 p.m., respectively, making the day length 15h 13m 32s. On December 21, 2009 (the winter solstice) ["http://www.timeanddate.com/worldclock/astronomy.html?n=64&month=12&year=2009&obj=sun&afl=-11&day=1"] the sunrise and sunset times are 7:15 a.m. and 4:23 p.m. respectively, making for a day length of 9h 7m 54s. The problem here lies in taking the sums of the two solstices' day lengths. Ideally, they should come out to 24h 0m 0s exactly (or within a minute or so), but this particular sum stands at 24h 21m 26s. Something has to account for the additional 20+ minutes. I imagine it would have to do something with adding the sums of all 365 (or 366 if it's a leap year) day lengths, and making sure it adds up to the product of 12 and 365 or 366.
Conclusion from #1b: if it is true that nighttime is shorter at the summer solstice than daytime at the winter solstice, then one might have to conclude that, to make up for this discrepancy, there must be more days of extreme shortness in the winter than days of extreme length in the summer.
Math problem #2 (a real one, with simple calculations instead of scientific debates): Your starting point (d=0) is the front of the northbound left-turn lane on Ridge Ave in Chicago intersecting with Howard St. Your starting time (t=0) is the instant the green arrow shows, allowing you to turn left. Your ending point is the intersection of Howard St and Western Ave, a distance of 0.3 miles from the starting point. Your ending time is the instant the westbound light at the Howard/Western intersection turns yellow (still TBD, largely due to the cell-phone ban while driving in Chicago, I presumably can't carry a stopwatch with me while driving) Calculate the following: the exact time between green arrow (at t=0) and the yellow light (at t=n); and the speed necessary to arrive at the Howard/Western intersection before the light turns yellow. [It would probably help to have a more exact distance; 0.3 miles is much too vague--ideally I'd be looking for something in units of feet or meters.] Also, be sure to account for amount of time needed to complete the left turn in the Howard/Ridge intersection.
For the record, I'm gonna say something around 40-45 miles an hour. Since the speed limit on Howard is 30, I believe (it could also be 25), making it through the Western Ave intersection off a left turn onto Howard from Ridge is most likely unattainable.
No comments:
Post a Comment