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1775, "pertaining to thrown objects," ultimately from Greek ballein "to throw" (see ballistics). Of rockets or missiles (ones that are guided while under propulsion, but fall freely), from 1949. Ballistic missile first attested 1954; they attain extreme heights, hence figurative expression go ballistic (1981) "become irrationally angry."
To become very angry and irrational; blow up, hit the ceiling: Either way, some constituents will go allisti/ Henry George would go allisti over the idea of reopening the capital gains tax break for real estate
[mid-1980s+; fr the extreme height attained by a ballistic missile, and the idea that upward motion is associated with anger]