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In The Fellowship of the Ring, the hobbit Peregrine Took (Pippin for short) drops a rock into a well while the travelers are in the caves of Moria. This wakes a balrog (a bad thing) and causes all kinds of trouble. Pippin heard the rock hit the water 7.5 s after he dropped it .

1. Ignoring the time it took the sound to get back up, how deep it the well?
   
2. If the speed of sound is 340 m/s (it was pretty cool in that part of Moria), was it OK to ignore the time it takes sound to get back up? Discuss and support your answer with a calculation.

Note to the instructor: Note the difference between this problem and the traditional one. In the traditional problem, one might ask first: "How long does it take for the object to fall?" Next, we would ask: "How long does it take the sound to get back up?" Finally, we would ask: "How long after dropping the object did he hear the splash." The way it is phrased here is more realistic and introduces two important ideas: the idea of approximation as a good way to get a "first cut" answer, and the idea that how you do the calculation depends on how accurately you need to have the answer.

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Page last modified October 8, 2002: K05