The Barometer & lateral thinking

Has always been a classic, so I will reproduce it as I got it. The I in the story is not me, but a professor…here goes

Some time ago I received a call from a colleague, who asked if I would be the referee on the grading of an examination question. He was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would if the system were not set up against the student.

The instructor and the student agreed to an impartial arbiter, and I was selected. I went to my colleague's office and read the examination question: "Show how it is possible to determine the height of a tall building with the aid of a barometer."

The student had answered: "Take the barometer to the top of the building, attach a long rope to it, lower it to the street, and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."

I pointed out that the student really had a strong case for full credit since he had really answered the question completely and correctly. On the other hand, if full credit were given, it could well contribute to a high grade in his physics course. A high grade is supposed to certify competence in physics, but the answer did not confirm this. I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed, but I was surprised when the student did.

I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said no. He had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on. In the next minute, he dashed off his answer, which read:

"Take the barometer to the top of the building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula x=0.5*a*t^2, calculate the height of the building."

At this point, I asked my colleague if he would give up. He conceded, and gave the student almost full credit. In leaving my colleague's office, I recalled that the student had said that he had other answers to the problem, so I asked him what they were.

"Well," said the student. "There are many ways of getting the height of a tall building with the aid of a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building, and by the use of simple proportion, determine the height of the building."

"Fine," I said, "and others?"

"Yes," said the student." There is a very basic measurement method you will like. In this method, you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units.

"A very direct method."

"Of course. If you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of g at the street level and at the top of the building. From the difference between the two values of g, the height of the building, in principle, can be calculated."

"On this same tact, you could take the barometer to the top of the building, attach a long rope to it, lower it to just above the street, and then swing it as a pendulum. You could then calculate the height of the building by the period of the precession".

"Finally," he concluded, "there are many other ways of solving the problem. Probably the best," he said, "is to take the barometer to the basement and knock on the janitor’s door. When the superintendent answers, you speak to him as follows: 'Mr Janitor, here is a fine barometer. If you will tell me the height of the building, I will give you this barometer.'"

At this point, I asked the student if he really did not know the conventional answer to this question. He admitted that he did, but said that he was fed up with high school and college instructors trying to teach him how to think.

Finito- This is what lateral thinking is all about.

I decided to check this story (has its origin 1964!!!) out a bit and see who came up with this piece.
The results are interesting

It does not stop here - So many others worked on this problem and came up with even more unique solutions – like (Thanks & credits to all those who thought laterally…)

Walk away from the building with the barometer at arm's length. Once the apparent height of the barometer is the same as the building’s, measure the distance from the building and the height of the barometer and use a little trigonometry.

On a sunny day, place the barometer on the ground. Mark both ends. Stand the barometer upright on the mark closer to the sun, so the shadow will be approaching the other mark. Note the exact time when the shadow reaches the other mark. On the following sunny day, mark the end of the shadow cast by the building at exactly that time. Measure the distance from there to the building. This is the height of the building. Note: The accuracy of this technique depends on the number of days between consecutive sunny days

Hold the barometer one foot in front of yourself and find a position where the building appears to be the same size as the barometer. Now measure the distance to the building (in feet) and multiply by the height of the barometer

Go to a local shop and trade the barometer for the longest measuring tape they have. Take the tape onto the roof of the building. Holding one end, drop the other end over the edge of the building. Raise the measuring tape until the far end is just touching, not resting on, the ground. Read the height of the building from the measuring tape. Note: For particularly tall buildings, this may require a particularly good hardware store.

Hold the barometer straight in front of you and drop it. Measure, very carefully, how long it takes to hit the ground. Go up on the roof and hold the barometer in the same position. Drop it and measure, again very carefully, how long it takes to hit the roof. Since gravity falls off as the square of the distance from the centre of the planet, you can use the difference in times to calculate the height of the building relative to the distance from the base of the building to the centre of the planet. The local library can provide you with the distance to the centre of the planet in the required units. Note: The ratio of the times is the same as the ratio of the distances from the drop points to the centre of the planet.

Drop (and shatter) the mercury barometer at the base of the building on a windless day. Measure the increase in the mercury vapour concentration at the top of the building. Solve the diffusion equation to determine the distance from the shattered barometer to the top of the building.

Place the barometer on the ground floor of the building. Seal all the building's doors and windows. Fill the building with water. Read the pressure measurement from the barometer. This gives the weight of a column of water the same height as the building. Use this and the ratio of the density of mercury to the density of water to calculate the height of the building. Note: It is common courtesy to evacuate the building before using this technique

Go to all the local gift shops. Look for a fancy souvenir barometer, the kind which shows important local landmarks. Find one, which shows the heights of local buildings and considers this building important enough to be listed. Use this barometer.

Clap the barometer against the top of the building. Measure the time taken to hear the echo from the ground. Find the height of the building by multiplying half the echo delay by the velocity of sound

Walk back a measured distance from the building. Using any convenient means, throw the barometer at the top of the building. (Use trial and error until you get the aim right) Measure the angle from the ground and the initial velocity, account for wind and air resistance, use several formulae, and be prepared to account for why you just smashed the sh*t out of the professor's new barometer.

And many more….

The expected, boring, orthodox answer -

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

Picture Courtsey - Barometerworld UK