You drop a stone into a deep well and hear it hit the bottom 4.40 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 343 m/s in air. How deep is the well?
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To find the depth of the well, we need to consider the time it takes for the stone to fall and the time it takes for the sound to travel back up.
1. First, let's find the time it takes for the stone to fall to the bottom of the well. We know from the problem that it takes 4.40 seconds in total, so we need to subtract the time it takes for the sound to travel back up. Let's call this time "t."
2. The speed of sound in air is given as 343 m/s. Since the sound has to travel to the bottom of the well and back, the total distance it travels is twice the depth of the well.
3. Using the formula d = v * t, where d is the distance traveled, v is the speed of sound, and t is the time taken, we can write the equation d = 2 * v * t.
4. We can rearrange this equation to solve for "t." Dividing both sides by 2v, we get t = d / (2v).
5. Now, substitute the given values into the equation. t = 4.40 s, v = 343 m/s.
6. Rearrange the equation to solve for "d." Multiply both sides by 2v and you get 2vt = d. Now substitute the values into the equation, d = 2 * (343 m/s) * (4.40 s).
7. Evaluate the expression to find the depth of the well. d = 2 * 343 m/s * 4.40 s = 3010.4 m.
Therefore, the depth of the well is approximately 3010.4 meters.