The Height Of A Building

A question in a physics examination at the University of
Copenhagen was: "Describe how to determine the height of a
skyscraper with a barometer".

One student answered: "You tie a long piece of string to the
neck of the barometer and then lower the barometer from the roof
of the skyscraper to the ground. The length of the string plus
the length of the barometer will equal the height of the
skyscraper."

This answer so incensed the tutor that he failed the student.
The student appealed to the university on the ground that his
answer was indisputably correct. So the university appointed an
impartial arbiter, a visiting American professor called Alexandra
Calandra, of the University of Washington.

Dr Calandra ruled that although the answer was technically
correct, it did not display any noticable knowledge of physics;
and to resolve the matter, he called the student in and gave him
five minutes in which to answer the question verbally in a way
that showed familiarity with the basic principles of physics.

For four minutes there was complete silence. The student sat
there frowning, deep in thought. Dr Calandra told him that his
time was running out, to which the student replied that he had
several relevant answers to the question, nut could not make up
his mind which one of them was best.

"You had better hurry up." said Dr Calandra.

"All right then," said the student. "You take the barometer up
to the roof of the skyscraper, drop it over the edge, and measure
the time it takes to reach the ground. The height of the
building can then be calculated in terms of the formula:-

          2
 H = 1/2gt

(height = one half times gravitational constant times time
squared). Unfortunately this procedure might destroy the
barometer.

If the sun happens to be shining, you could measure the length of
the barometer and then stand it on it's end and measure the
length of it's shadow. You could then measure the length of the
skyscraper's shadow. It would then be a matter of simple
proportional arithmetic to determine the skyscaper's height.

If the skyscraper has an external fire escape, you could walk up
it marking off the height in barometer lengths. Then it is
simply a matter of counting the marks and multiplying the count
by the length of the barometer.

If you wanted to be highly scientific you could tie a short piece
of string to the barometer and swing it like a pendulum, first at
ground level, and then on the roof, and calculate the height from
the difference in gravitational restoring force.

The obvious solution is to measure the barometric pressure at
ground level and then on the roof of the skyscraper. You could
then convert the difference to metres. However the flaw in this
method is that most barometers would have insufficient resolution
to accurately detect the difference in barometric pressure over
such a relatively small difference in height as is represented by
the height of most skyscrapers.

However I really believe that the easiest method would be to go
to the caretaker of the skyscraper and say "If you tell me how
high the skyscraper is, I will give you this beautiful
barometer."