How Deep Is the Cavern if a Pebble Takes 1.8 Seconds to Hit the Water?

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To determine the depth of the cavern, the explorer drops a pebble and measures the total time of 1.8 seconds until the sound of the pebble hitting the water is heard. The speed of sound in the cave is 345 m/s, which is crucial for calculating the time it takes for the sound to travel back up. The problem requires separating the time it takes for the pebble to fall and the time for the sound to return, leading to the equation t = 1.8 - d/Vs. The correct approach involves using kinematic equations to relate the depth of the cavern to the time taken for both the pebble and the sound. The final calculated depth of the cavern is 15 meters.
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Homework Statement


An explorer drops a pebble into a cavern to see how deep it is. At 1.8 seconds, the explorer hears the pebble hit the water. The speed of sound travels at 345 m/s in the cave. How deep is the cavern?

This seems like a kinematic question but I can seem to get the right answer. Does anyone have any idea how to approach this? The answer is 15 meters btw.


Homework Equations



The kinematics equations.

The Attempt at a Solution



I've tried letting the time it takes the pebble to hit the ground to be 1.8 minus the time it takes for the sound to come back up. So I had something like t=1.8-d/Vs, where Vs is the speed of sound. I tried plugging that time into a kinematic formula but I had no luck.
 
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What do you know about the distance that the pebble falls and the distance that the sound wave travels? How does the time it takes the pebble to reach the surface depend on the drop height h?
 
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