I was asked this question at a job interview. Suppose you are standing near a skyscraper and only have a barometer. How can you determine the height of the skyscraper?

I said that I would check the barometer reading at ground level, then ride an elevator to the top of the building and read the barometer again. There is probably a science formula that I could use that tells the change in altitude by the change in barometric pressure.

However, I couldn’t remember any such formula, so I would just estimate the building height based on the number of floors. What do you think? Is there a formula to use?

That is how atlimeter watches work. there are formulas but I don’t know them any more. you might look for a relationship of how pressure changes with altitude

Well, the correct answer is to check the pressure at the bottom of the building, ride the elevator to the top, then measure the pressure there. Then, using a formula I have forgotten you would determine the height of the building.

Since I can’t remember the formula, what I would do would be to ride to the top of the building, drop the barometer off the side and time how long it took to hit the ground. Then, I would determine the height using the formula:
s=(a * t^2) / 2

where “a” is the acceleration constant (32 ft/s^2 or 9.8 m/s^2) and t is the time it took to fall (in seconds). “s” is the height of the building.

There are other ways to do it as well. You could measure the height of the barometer then put it on the ground next to the building and measure the length of its shadow. Then, you can measure the length of the building’s shadow and determine the building’s height through trigonometry.

Or, you can always go to the building maintenance supervisor and say “Hey, I’ll give you this brand new barometer if you will tell me how tall this building is.”, but that’s probably cheating.

“Drink your coffee! Remember, there are people sleeping in China.”

Be happy. Any job that asks dopey questions like that at the interview can’t be that good a job. Unless the job is measuring the heights of buildings with barometers.

change in pressure = - change in height * density * gravity

density of air at STP is around 1.3 Kg/m^3 and acceleration of gravity is 9.8 m/s^2. Use the formula to find change in height but be careful. Most barometers are read in mb millibars and this formula uses pascals. 1 mb = 100 Pa.

“Teaching without words and work without doing are understood by very few.”
-Tao Te Ching

where p is pressure, h is altitude (be consistent with your ‘1’ subscripts!), g[SUB]o[/SUB] is acceleration due to gravity = 9.8 m/s[SUP]2[/SUP] or 32.2 ft/s[SUP]2[/SUP] on Earth, R is the specific gas constant = 287 J/(kg-K) or 1716 ft-lb/(slug-[SUP]o[/SUP]R) for air, and T is temperature in Kelvin or degrees Rankine.

Take the Barometer to the top of the building and throw it off. Use your watch to count the seconds it takes to hit the ground. Use the formula for the distance an object travels when accelerated at 1g for that number of seconds.

Take the barometer into the building and find the building manager. Tell him that you will trade him the barometer if he tells you how high the building is.

Tie the barometer to a long string and lower over the side of the building until it touches the ground. Mark the string, pull it back up and measure from the end of the string to the mark.

Measure the height of the barometer. Bribe the building’s window washers to lower you slowly down the side of the building on their platform. As you go, mark off the building in “Barometer Height units”. When you get to the bottom, multiply to get the height of the building.

Measure the height of the barometer and the length of the shadow cast by the barometer and by the building at the same time. Use simple geometry to calculate the height of the building.

Ok, I cheated a little, you did you had only the barometer. But everyone carries a watch and string, don’t they?

Ugly (I’m pretty sure I read these answers somewhere a long time ago, but I can’t remember when or where. If anybody knows, please give credit where due.)