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

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SUMMARY

The discussion centers on calculating the depth of a cavern based on the time it takes for a pebble to hit the water and the sound of the impact to travel back to the explorer. The pebble takes 1.8 seconds to reach the water, and the speed of sound in the cave is 345 m/s. The correct depth of the cavern is established as 15 meters. The problem involves understanding kinematic equations and the relationship between the time taken for the pebble to fall and the sound to return.

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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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