You could use the GPS in your cell phone to get the height of the barometer above sea level while it's on the roof, then put it on the ground and get a second reading, then just subtract the two.
You could throw the barometer over the building and then calculate the trajectory and the time it took it to land on the other side, but the math required to do that is way too complicated for me to figure out.
So you don't risk environmental contamination from the mercury inside the column (inherent in many of these suggestions), then go down to the local building department and pull the blueprints for the building.
It does involve the barometer, at least insofar as safely storing it and protecting the environment from a nasty mercury spill.
Obviously your sarcasm detector was miscalibrated, as I was commenting on the disastrous toxic exposure risks involved in some of the suggestions (dropping it off the building, launching it over the building, etc.)
Consider it recalibrated (your sarcasm detector, not the barometer).
Max re: "But that doesn't involve using the barometer, which is a key requirement for the exercise."
Convince the records office clerk that the barometer is actually a very valuable antique watch. Then bribe him or her with the watch to go right away and get the blueprints without delay, so you'll have enough time to stop at a barometer store and buy a new one on the way back to the building site.
Let's try again. first is it an aneroid or mecury barometer? If mecury then it will have a scale. Use that scale as the basis of developing a measuring stick or string. Then use the string to produce a 45 degree right angle triangle, along the top of a table and the height of the string. Then sight the top of the building along the hypotenuse of the triangle. Knowing the distance away from the building you can calculate the height of the tall building. If the building is very tall then it is easy to make both 45 and 60 degree triangles and use them to sight the top of the tall building. Now knowing the distance apart of the two sighting positions you can calculate the height of the building and the distance you are away from it.
If it is an aneroid barometer then make a simple parachute and drop the barometer attached to it from the top of the tall bulding. The barometer and parachute will quickly reach terminal velocity, so have a colleague a couple of floors of easily measurable distance down measure the time it takes to pass him/her and also the total time to reach the ground. The calculation of height is then trivial. This method avoids the problem of the calculation when throwing just the barometer off of the very tall building and a period of gravitational acceleration and then terminal velocity are involved.
Buy a cheap laser or for that matter any flashlamp with a decent beam. Move some measured distance from the base of the building. Point the laser at the top of the building and measure the angle that the laser/flashlamp is tilted. A simple trig calculation, using the length of the laser and the distance it is tilted, the accuracy can be increased by intercepting the beam a couple of feet from the ground. The tangent of the angle and the distance from the building will allow its height to be calculated.
Best done at night but be careful to avoid being hit by a barometer that some idiot has dropped from the top of the building
Max, you may want to lookup one of the Communications Society event I chaired:
Nov 2012: Technologies for Location Determination in Indoor and Urban Environments.
The speaker from NextNav (formerly @Trimble Navigation) does allude to atmospheric pressure measurement as one of the reliable ways (need 10Pa resolution). This can be accomplished by MEMS pressure sensors in a smart phone BUT it needs to be quite precise and must correlate to a reference system.
Max, I would like to add another: have the students measure the reading on ground floor, and then climb two more floors, take readings in each and get the delta in pressure between floors. Count the number of storeys in the building and use USGS data charts to get the exact height. There will be some minor inaccuracy in this since the pressure drop vs. elevation curve is not linear, quadratic.
All Good suggestions. Another one I read was to set stand at the bottom of the building holding the barometer -- remotely detonate an explosion at the top of the buliding -- and measure the amount of time it takes the pressuse wave to register on the barometer :-)
Has anyone mentioned the correct use? Measure air pressure at bas of building, then air pressure at the top. Find the difference and use that to compute the altitude... Of course, you might need to take a trip to the beach to find the presseure at sea level, too...
Max, re: "Drop the barometer off the top of the building, measure how long it takes to hit the ground, and use this value to calculate the height of the building."
Many long years ago, I had a summer job working in the glorious Pacific Northwest forests. Part of the job involved climbing fir trees to pick the cones, which would be used in research plantings.
One day a buddy and myself were each in old growth Douglas fir trees, up in excess of 200 feet. To keep ourselves amused while picking, we yelled back and forth between trees to collaboratively use our calculus knowledge to figure out how fast we'd be going when we hit the ground from that height.
@Duane: To keep ourselves amused while picking, we yelled back and forth between trees to collaboratively use our calculus knowledge to figure out how fast we'd be going when we hit the ground from that height.
You certainly knew how to have fun in those days :-)