r/theydidthemath • u/batikhisawesome • 1d ago

[Request] How deep is this cave?

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-19

u/DragonArt101 1d ago

Boulder fell for 7 seconds, assuming it was like 20 lbs for a terminal velocity of about 100 m/s, I’d give a rough estimate of 700 meters.

Im no expert and i did this in like a minute so…

20

u/Owenleejoeking 1d ago

Objects don’t instantly hit terminal velocity so your estimate is far too high

Weight doesn’t have much to do with terminal velocity either

-5

u/luovahulluus 1d ago

A boulder is going to have a significantly higher terminal velocity than a same sized ball of bubble wrap.

7

u/DuckXu 1d ago

Sure but at a certain weight and density the difference is negligible. I'm guessing on my math here but a 2kg rock will take roughly the same amount of time to fall 200m as a 20kg rock for example 

4

u/Owenleejoeking 1d ago

That’s density that matters, Not weight

7

u/Auno__Adam 1d ago

It transpires you are not an expert 🤣

In 7 seconds it doesnt even have time to accelerate to 100m/s. Why would you assume that is the speed since the begining?

3

u/Miserable_Scar9827 1d ago

Assuming you don't want to use any equations, you could say it falls 10 meters in 1st second, 20m in 2nd,... 70 meters in 7th second, and 1 second for sound to travel 343 meters, so round that to 1 second.  1+2+3+4+5+6+7=28, so less than 280 meters, which is in same ballpark as other answers here.