hard hat n.

Old English heard "solid and firm, not soft," also, "difficult to endure, carried on with great exertion," also, of persons, "severe, rigorous, harsh, cruel," from Proto-Germanic *hardu- (source also of Old Saxon hard, Old Frisian herd, Dutch hard, Old Norse harðr "hard," Old High German harto "extremely, very," German hart, Gothic hardus "hard"), from PIE *kortu-, suffixed form of root *kar- "hard."

Meaning "difficult to do" is from c. 1200. Of water, in reference to the presence of mineral salts, 1650s; of consonants, 1775. Hard of hearing preserves obsolete Middle English sense of "having difficulty in doing something." In the sense "strong, spiritous, fermented" from 1789 (as in hard cider, etc.), and this use probably is the origin of that in hard drugs (1955). Hard facts is from 1853; hard news in journalism is from 1918. Hard copy (as opposed to computer record) is from 1964; hard disk is from 1978; the computer hard drive is from 1983. Hard times "period of poverty" is from 1705. Hard money (1706) is specie, silver or gold coin, as opposed to paper. Hence 19c. U.S. hard (n.) "one who advocates the use of metallic money as the national currency" (1844). To play hard to get is from 1945. Hard rock as a pop music style recorded from 1967. To do something the hard way is from 1907.

Old English hæt "hat, head covering" (variously glossing Latin pileus, galerus, mitra, tiara), from Proto-Germanic *hattuz "hood, cowl" (source also of Frisian hat, Old Norse hattr, höttr "a hood or cowl"), of uncertain etymology; it has been compared with Lithuanian kuodas "tuft or crest of a bird" and Latin cassis "helmet" (but this is said to be from Etruscan).

To throw (one's) hat in the ring was originally (1847) to take up a challenge in prize-fighting. To eat one's hat  (1770), expressing what one will do if something he considers a sure thing turns out not to be, is said to have been originally eat Old Rowley's [Charles II's] hat.