this post was submitted on 04 Feb 2024
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Conservation of momentum.
You don't suddenly stop moving with the Earth just because you're no longer standing on terra firma. Like, if you throw a ball it doesn't just suddenly fall straight to the ground once it leaves your hand.
Plus, in a hot air balloon you're still in the atmosphere... Which is also moving. But even if you were in the total vacuum of space, the above applies and you still wouldn't remain stationary without actively countering the momentum you already have. And then you'd just be pulled in by gravity, unless you actively counter that too. And all that countering of forces is way more costly with fuel than simply accounting for the fact you're already moving at super high speeds along with the rotation of the planet.
Conservation of momentum doesn't really come into it for this scenario. A balloon is a huge, low-density object so it's basically always going to go at the same speed of the wind at whatever height it's at.
The only way conservation of momentum could matter is if the balloon could get out of the atmosphere so it wasn't being pushed around by the wind. But, of course, the way a balloon works is that it goes up as long as its density is lower than the density of the atmosphere it's in. That means it's always going to be stuck in fairly thick atmosphere, and always subject to the winds.