Physics exam ...

The following was really a question asked on a physics exam, at the University of Copenhagen: Describe how to determine the height of a skyscraper with a barometer. One student answered: you tie a long piece of string to the base 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 equals the height of the building.

This highly original answer so outraged the examiner that the student was immediately dismissed. He appealed his basic rights, arguing that his answer was indisputably correct, and the university appointed an independent arbitrator to decide the case. The arbitrator ruled that the answer was indeed correct, but showed no perceptible knowledge of physics. To resolve the issue, it was decided to invite the student back in and allow him six minutes in which to give an oral answer that showed at least a minimal familiarity with the basic principles of physics.

For five minutes, the student sat quietly, head forward, lost in thought. The referee reminded him that time was running, to which the student replied that he had some extremely relevant answers but could not decide which to use. When advised to hurry up, he replied as follows:

First, 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 be calculated with the formula H=0.5g x t2. The barometer would be gone though! Or, if the sun is shining, you could measure the height of the barometer, raise it, and measure the length of its shadow. Then measure the length of the shadow of the skyscraper, after that it is a simple matter to calculate the height of the skyscraper using proportional arithmetic. But 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 on the ground and then on the roof of the skyscraper. The height corresponds to the deviation of the gravitational restoring force T=2pi2 (l/g).

Or, if the skyscraper has an external emergency staircase, the easiest way would be to climb up there, tick off the height of the skyscraper in barometer lengths and add up at the top.

But if you just want a boring and orthodox solution, then of course you can use the barometer to measure the air pressure on the roof of the skyscraper and on the ground and convert the difference in millibars to calculate the height of the building. But, since we are constantly being asked to exercise independence of mind and use scientific methods, it would no doubt be much easier to knock on the janitor's door and tell him, "If you want a nice new barometer, I'll give you this one, provided you tell me the height of this skyscraper.