Throw Up, Spit, Vomit
If you put dirt in your mouth you're going to throw up. That's just a fact.
That's pretty much what throwing up feels like too, right? Like a bunch of dirt coming out of your mouth. Barf.
と
は, つ
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When you throw up it sounds like you're shouting, "HA (は)!" Then all the dirt-puke comes out in a wave. It's less of a laugh ha and more of an oh no I'm throwing up ha.
Imagine the sound you made the last time you threw up. It sounded like you were saying HA from the bottom of your tummy.