A student is sitting his Physics exam, and quite an important one at that---maybe his final degree paper or his Oxford Entrance. Anyway, one of the questions on the paper was to the effect of:
``Q: How could one measure the height of a building using a barometer?''
Being a wit, in the exam this chap puts:
``A: Drop the barometer from the top of the building and time its descent. Using the formula `s = ut + a(t^2)/2' and knowing `a' which is `g' we can calculate the height of the building with reasonable accuracy.'' He then goes on to describe in more detail the method he would use."
The examiners were a little concerned. Here was one of their star students giving an answer they hadn't at all expected. So they decided to call him in and give him an oral test to decide whether or not to allow the answer which they did admit was perfectly valid.
So they called him in and told him he had 15 minutes to make his case. For ten minutes he said nothing but scribbled away furiously. After these ten minutes the atmosphere was getting a little tense---this was meant to be an oral after all, and his degree (or whatever) depended on it. When they pointed this out to him he said that he was just trying to get his thoughts in order as there were so many possible solutions. Here are some of the ones he came up with:
``1: What you wanted me to do, of course, was measure air pressure at the top and bottom of the building, and from the difference and knowing the pressure exerted by a column of air of unit height I should be able to calculate the height of the building. But I thought that would be terribly inaccurate and the answer I gave in the exam and the following ones are all potentially more accurate."
2: Measure the length of shadow cast by the bulding and by the barometer on a sunny day. Knowing the actual height of the barometer one can compute the height of the building.
3: Tie the barometer to the end of a long bit of string and lower the barometer from the top of the building to the ground. Measure the amount of string payed out and you have the height of the building.''
He then gave several more but ended with:
``The best method by far, though, would be to go to the building's janitor and say `If I give you this shiny new scientific barometer will you tell me how high this building is?' ''
The student passed his exam.