You are traveling in the fabled Mines of Moria when you come across an open wate

Question

You are traveling in the fabled Mines of Moria when you come across an open water well in the stone floor of a tunnel. To find out how seep the well is, you drop a stone in to the well and count the seconds until you hear the splash. If you hear the splash a time after you drop the stone, roughly what is the depth D of the well? Be sure you describe any approximations you have to make to do the problem. [Hint: The speed of sound is = 340 m/s. Let the actual time of the splash be . This is different from : why? I strongly recommend that you solve for D symbolically before plugging in numbers (or you will likely become totally lost), but pay very careful attention to signs: in particular, make sure that D is positive. If you end up with two possible answers, select the answer that leads to a positive value for . Why is a negative absurd?)

Explanation / Answer

Let D be the depth of the well

Let t be the time taken for stone to reach at the bottom

D = 1/2*g*t^2

t = D/4.9

Now, The speed of sound is = 340 m/s

Total time taken to hear the splash after dropping the stone = 1 second

hence time taken by the sound to reach us = 1 - t = 1 - D/4.9

So, D = Speed of sound * (1 - D/4.9)

D = 340*(1 - D/4.9)

D = 340 - 69.4D

70.4D = 340

D = 4.83 m

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