## Frank Morgan's Math Chat |

April 20, 2000

**ANSWER. **It is not a good approximation on a warm day when the temperature
suddenly plummets at 11:59 pm. Since such drastic and precisely timed
events are rather rare, it is usually a pretty good approximation.

Mathematically, the approximation is good because Earth's warming and cooling behave similarly, as pointed out by John M. Sullivan. The approximation would be worse if the Earth warmed up linearly and cooled off exponentially, like a pot of tea.

**QUESTIONABLE MATHEMATICS.** Eric Brahinsky reports that "the "Ripley's
Believe It or Not!" feature, published in the *San Antonio Express-News* on
04/10/00, claimed:

Believe It or Not! TWO OFFICE WORKERS SURVIVED AFTER THE ELEVATOR THEY WERE RIDING INSIDE New York City's EMPIRE STATE BUILDING FELL 40 STORIES AT A RATE of 1,395.5 ft. PER SECOND - BEFORE FINALLY STOPPING ON THE 4TH FLOOR!"

Brahinski estimates that 40 stories is about 500 feet. Even if the elevator were in free fall the whole way, its final velocity would be just the square root of twice the acceleration (32 ft/sec/sec) times the distance, or only about 180 feet per second. Brahinsky concludes, "So unless some information was omitted (e.g., pranksters had affixed a rocket engine to the top of the elevator...), I think Mr. Ripley had better do his homework."

For another question on falling elevators, see Math Chat of February 18, 1998.

Readers are invited to send in more examples of questionable mathematics.

**NEW CHALLENGE** (Joe Shipman). On ABC TV's "Who Wants to be a Millionaire,"
after winning $250,000, you are guaranteed to keep $32,000, and you go on
to $500,000 and $1,000,000 questions. After hearing a question, you can
answer correctly and win the new amount, walk away with your previous
winnings, or answer incorrectly and leave with $32,000. How sure should you
be of your answer to the $500,000 question to answer (to maximize your
expected winnings). Assume no "lifelines" (opportunities for special
outside help) remain.

Send answers, comments, and new questions by email to
Frank.Morgan@williams.edu, to be eligible for* Flatland *and other book
awards. Winning answers will appear in the next Math Chat. Math Chat
appears on the first and third Thursdays of each month. Prof. Morgan's
homepage is at www.williams.edu/Mathematics/fmorgan.

THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).

Copyright 2000, Frank Morgan.