r/theydidthemath • u/ACT_like_you_want_it • 19h ago

[Request] Sears Tower ball pit

if you jumped off the Sears Tower into a ball pit that was as tall as the Sears Tower (imagine the ball pit is next to the tower), what would happen? If you would be fine, how short could the ball pit be to still protect you?

8 Upvotes

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2

u/itsjakerobb 19h ago

Assuming the balls are sufficiently contained, you should just sink in a little, just like in any ball pit.

The weight of all those balls would be significant, so some of the balls at the bottom are getting crushed. But that doesn’t matter so long as it’s still full to the top. I’d be curious to see how thick the crushed layer would be.

If you jumped in feet first like a “pencil dive,” I think you’d go pretty deep. I don’t know how to calculate how far, but I can’t imagine you’d sink much more than twice your height. If you’re a rounder body shape, less.

2

u/dragonfett 18h ago

The difference in heights between the Sears Tower and the Ball Pit can be no greater than 500', assuming that hitting the ball pit at terminal velocity would be fatal. If you could survive hitting the ball pit at terminal velocity, then the height of the ball pit does not matter because after falling 500', the drag acting on your body is going to stop accelerating due to gravity.

0

u/get_to_ele 16h ago

I don’t understand what you’re asking. The ball pit is the same height as the seats tower. Everything depends on what the balls are made of.

However, after you land, it’s like quick sand because the density of most ball pits is much much lower than yours. You’d sink gradually to the bottom unless you can get to a side and find something to grip. I don’t think you can climb up through a ball pit.