How to determine the height of a skyscraper with a barometer



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The following question appeared in a physics degree exam 
at the University of Copenhagen:

"Describe how to determine the height of a skyscraper with a barometer."

One enterprising student replied: "You tie a long piece of string to 
the neck of the barometer, 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 building."

This highly original answer so incensed the examiner that the student
was failed immediately. The student appealed, on the grounds that his 
answer was indisputably correct, and the university appointed an 
independent arbiter to decide the case.

The arbiter judged that the answer was indeed correct, but did not 
display any noticeable knowledge of physics. To resolve the problem it 
was decided to call the student in and allow him six minutes in which 
to verbally provide an answer, which showed at least a minimal 
familiarity with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in thought.

The arbiter reminded him that time was running out, to which the student
replied that he had several extremely relevant answers, but couldn't 
make up his mind which to use.

On being advised to hurry up the student replied as follows:

"Firstly, you could 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 worked out 
from the formula H = 1/2gt squared (height equals half times gravity 
time squared). But bad luck on the barometer."

"Or if the sun is shining you could measure the height of the 
barometer, then set it on end and measure the length of its shadow. 
Then you measure the length of the skyscraper's shadow, and thereafter 
it is a simple matter of proportional arithmetic to work out the height
of the skyscraper."

"But if you wanted to be highly scientific about it, 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 of the skyscraper. The 
height is worked out by the difference in the gravitational restoring 
force (T = 2 pi sq. root of l over g)."

"Or if the skyscraper has an outside emergency staircase, it would be 
easier to walk up it and mark off the height of the skyscraper in 
barometer lengths, then add them up."

"If you merely wanted to be boring and orthodox about it, of course, 
you could use the barometer to measure air pressure on the roof of the
skyscraper, compare it with standard air pressure on the ground, and 
convert the difference in milliners into feet to give the height of 
the building."

"But since we are constantly being exhorted to exercise independence of
mind and apply scientific methods, undoubtedly the best way would be to
knock on the janitor's door and say to him 'I will give you this nice
new barometer, if you will tell me the height of this skyscraper'."

The arbiter re-graded the student with an 'A.'
                                                                           

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[Contributed by Peter]     

Rome did not create a great empire by having meetings...
they did it by killing everyone who opposed them.