How would you find out the height of a building using a barometer?

Remember the question "How would you find out the height of a building
using a barometer?"  This was supposedly asked on a physics exam.  The
answer that a physics teacher probably intended is a poor one -- you
can't read an ordinary barometer well enough to tell small changes in
altitude.  But people have produced *lots* of other answers.  And I for
one think this sort of thing is great fun.  One or two of these are
original with me as far as I know, by the way.

Oddly enough, this one isn't in the archive.  It does appear either in
James Fixx's "Games for the Superintelligent" or in the followup "More
Games for the Superintelligent"; about five answers are given there, as
I recall.

Here are nine solutions that don't involve reading the barometer.
(Yes, air resistance will spoil most of them if [Editor: "of" in the
original] the building is very tall.  In that case the teacher's
solution might be best after all.)

1. Drop the barometer off the roof or down a stairwell, and time the
   fall.

2. Drop the barometer off the roof or down a stairwell onto an impact-
   measuring device.  (Weigh it first.)

3. The inverse of 2: build a catapult that ejects things with a
   calibrated, adjustable force.  Fling the barometer from the catapult
   harder and harder until you know how much force will just get it to
   the roof.  (Weighing it first.  On this one, you'd better weigh what's
   left of it before *each* trial.)

4. Measure the length of the barometer, and walk up the stairs counting
   barometer-lengths along the wall.

5. Measure the length of the barometer and its shadow, and the shadow of
   the building.

6. Dangle the barometer from the roof or down a stairwell on a long
   cord, pull the cord back up, and measure its length.

7. Dangle the barometer from the roof or down a stairwell on a long
   cord, let it swing like a pendulum, and measure the swing period.

8. Find someone who knows the height of the building, and offer to give
   them the barometer in exchange for telling you the answer.

9. Find someone who knows the height of the building, and threaten to
   hit them with the barometer unless they tell you the answer.

-- Mark Brader <msb@sq.com>

You can tell the height of the building by comparing the shadows of the
building and the barometer.  If the barometer is placed at 90 degrees to
the ground, assuming that is also the angle of the building to the
ground.  Each will cast a shadow that is in relation to the heights of
the barometer and building.  Measure the height of the barometer and its
shadow and the shadow of the building.  The height of the building then
can be found.

-- NHR <nhr@aol.com>

This problem of measuring a building with a barometer is very old, and I
believe I have seen around a dozen solutions.  One of them was to use
the barometer to measure the risers on the stairs all the way to the
top.  Another was to go to the building manager and say, "Here's a nice
barometer you can have if you just tell me the height of the building."
Etc.

-- David Spero <mrrogers@igc.apc.org>

I've seen a number of those answers before - let's see how many I can
remember offhand.

1) The intended answer:  Measure the relative humidity at the top and
   bottom of the building.  Plug those numbers into some formula, which
   I don't know offhand.
2) Drop it from the roof and time its fall.
3) Lower it on a string from the roof till it touches the ground, then
   measure the length of the string.
4) Find someone who knows the height of the building and offer to give
   em the barometer if e will tell you.

-- Ed Murphy <zvyezda@ix.netcom.com>

[ Editor: a barometer measures air pressure, not humidity; the intended
  answer compares the air pressure at the top and the bottom of the
  building. ]