Given a measuring tape and a watch, how can you measure the height of the Sears Tower, or Bin ben?

QuoteOriginally posted by: jugantusGiven a measuring tape and a watch, how can you measure the height of the Sears Tower, or Bin ben?This sort of brainteaser requires a wholly unorthodox solution, one that could only emerge from a hopelessly bored nogooder who has no better thing to do than solve a problem that has probably been addressed in many varieties here and elsewhere much more than once.Here's my unorthodox solution:The watch is totally useless, not even good enough to measure the time of descent if something were to fall freely from the top of a tall building. So, we will sell this (presumably) expensive watch and with the money from the sale we will buy a diamond-toothed hand saw. We will then start cutting the Sears Tower at its base until it collapses and falls down. Assuming it does not shatter into pieces, we will then start measuring the length of the Sears Tower from one end to the other. We do so by repeatedly using the measuring tape. Hah, you thought I could not do the problem? Well, see for yourself.

QuoteOriginally posted by: dunrewppQuoteOriginally posted by: jugantusGiven a measuring tape and a watch, how can you measure the height of the Sears Tower, or Bin ben?This sort of brainteaser requires a wholly unorthodox solution, one that could only emerge from a hopelessly bored nogooder who has no better thing to do than solve a problem that has probably been addressed in many varieties here and elsewhere much more than once.Here's my unorthodox solution:The watch is totally useless, not even good enough to measure the time of descent if something were to fall freely from the top of a tall building. So, we will sell this (presumably) expensive watch and with the money from the sale we will buy a diamond-toothed hand saw. We will then start cutting the Sears Tower at its base until it collapses and falls down. Assuming it does not shatter into pieces, we will then start measuring the length of the Sears Tower from one end to the other. We do so by repeatedly using the measuring tape. Hah, you thought I could not do the problem? Well, see for yourself.Very good!Or how about: "Commit a bizarre and heinous crime at the top of the building (e.g., bind the victim with tape measure and stuff the watch in their mouth) then watch the newspapers for reports of the crime which will inevitably cite the height of the building. "

Give the watch to the responsible for the building maintenance and ask him the height.

If with watch you mean the watch there's in my iPhone 4, then just google Sears Tower and open the Wiki page. You will also discover that the actual name is Willis Tower.

I also googled "Bin ben" (with the typo) and found this interesting quote about the word "bin"Quote "Ibn" ("son of") seems to be spelled "ibn" when used at the beginning of a name, and "bin" when preceded by another bit of the name (Joe bin Bob, or just Ibn Bob). Or it's "Ibn" in the Middle east and "Bin" in north Africa. If somebody who actually knew something about Arabic names could confirm/give more details, it'd be swell. Note that in some families (mostly living in Morocco or France) it's spelled "ben".

QuoteOriginally posted by: DevonFangsI also googled "Bin ben" (with the typo) and found this interesting quote about the word "bin"Quote "Ibn" ("son of") seems to be spelled "ibn" when used at the beginning of a name, and "bin" when preceded by another bit of the name (Joe bin Bob, or just Ibn Bob). Or it's "Ibn" in the Middle east and "Bin" in north Africa. If somebody who actually knew something about Arabic names could confirm/give more details, it'd be swell. Note that in some families (mostly living in Morocco or France) it's spelled "ben".So this implies that Bin ben = "son of son"? ANd it might imply that Big Ben (Big son) is really an Islamic minaret?!?!

QuoteOriginally posted by: outrunAnother solution:Use the measuring tape to estimate the height / distance ratio like shown below, look at your watch, and say to the G&S interviewer "Oh my!, I see this interview has already taken more that 30 seconds, I need to catch a train, ..bye.."This won't work for Big Ben (no sun in London, so no shadows!). But if one did have some sun, then one could also calculate height based on the time it took the shadow of the top to move a tape-measured number of feet.

QuoteOriginally posted by: Traden4AlphaQuoteOriginally posted by: DevonFangsI also googled "Bin ben" (with the typo) and found this interesting quote about the word "bin"Quote "Ibn" ("son of") seems to be spelled "ibn" when used at the beginning of a name, and "bin" when preceded by another bit of the name (Joe bin Bob, or just Ibn Bob). Or it's "Ibn" in the Middle east and "Bin" in north Africa. If somebody who actually knew something about Arabic names could confirm/give more details, it'd be swell. Note that in some families (mostly living in Morocco or France) it's spelled "ben".So this implies that Bin ben = "son of son"? ANd it might imply that Big Ben (Big son) is really an Islamic minaret?!?!Yes, it does.

Prerequisites: The visitor has prior knowledge of measuring tapes and how to use them.1. Attach the watch to the end (or rather the beginning) of the measuring tape.2. Drop the watch weighter to the ground while still holding on to the other end of the tape.3. While letting the weight stay on the ground, put the tape towards the edge of the building; make sure it is stretched and read the result.According to wiki"Surveyors use tape measures in lengths of over 100 m (300+ ft)."

I am surprised nobody refered to the famous story about Niels Bohr (here). It is slightly different problem requires you to measure a tall building with only a barometer but ideas can be applied with this tape+watch problem as well.

One could also tie a knot on one end of the tape and use it as a pendulum to measure the pendulum period on the ground and on the top of the building (or make a pendulum out of both the tape and the watch as a weight if the tape itself wouldn't do - just reading the time would be a bit inconvenient). The pendulum period is proportional to the g-force (no idea why someone called an acceleration a force) and the height of the building h can be calculated from g_h = g_0 (R/(R+h))^2, where R is the Earth radius. Wouldn't work that bad for such high buildings, I think.Jugantus, wasn't the mention of Big Ben a hint to use the pendulum method?QuoteOriginally posted by: Traden4AlphaThis won't work for Big Ben (no sun in London, so no shadows!). You don't need the shadow to solve it from Thales' theorem. Just extend your arm and unfold the tape so that its top covers with the top of the building in the line of your sight.QuoteOriginally posted by: anilmagI am surprised nobody refered to the famous story about Niels Bohr (here). It is slightly different problem requires you to measure a tall building with only a barometer but ideas can be applied with this tape+watch problem as well.Well, to measure the hight with a barometer I would ask MacGyver to make it out of the watch and the tape for me... and then I would drop it from the top of the building :-Da.