Basically, picture a cherry bomb under a really strong teacup that stayed in one piece during the explosion and shot up in the air, but scaled up a whole lot.
There was a plan for this — [project orion](https://en.m.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)). It was scrapped for the obvious reason of excessive radiation contamination of the atmosphere and various treaties banning the detonation of nukes in the atmosphere.
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