"tear apart, cut open or off," c. 1400, rippen, "pull out sutures," probably from a North Sea Germanic language (compare Flemish rippen "strip off roughly," Frisian rippe "to tear, rip;" also Middle Dutch reppen, rippen "to rip") or else from a Scandinavian source (compare Swedish reppa, Danish rippe "to tear, rip"). Likely most or all of them are from a Proto-Germanic *rupjan- (from PIE root *reup-, *reub- "to snatch"). "Of somewhat obscure origin and history; it is not quite certain that all the senses really belong to the same word" [OED].
The meaning "to slash with a sharp instrument" is from 1570s. Intransitive sense of "be torn or split open" is by 1840. Related: Ripped; ripping. In old U.S. slang, "to utter strong language" (1772), often with out; hence "break forth with sudden violence." The meaning "to move with slashing force" (1798) is the sense in let her rip "allow something to go or continue unrestrained," an American English colloquial phrase attested by 1846.
At another time, when a charge was ordered one of the officers could not think of the word, and he shouted—'Let 'er rip!'—when the whole line burst out with a yell—'Let 'er rip!' and dashed in among the Mexicans, laughing and shouting this new battle cry. [from an account of Illinois volunteers in the Mexican-American War, in the Pensacola Gazette, March 29, 1851]
In garments we rip along the line at which they were sewed ; we tear the texture of the cloth; we say, "It is not torn; it is only ripped." More broadly, rip, especially with up, stands for a cutting open or apart with a quick, deep strike: as, to rip up a body or a sack of meal. Rend implies great force or violence. [Century Dictionary]
1711, "rent made by ripping or tearing," from rip (v.). The U.S. colloquial meaning "a rapid rush" is by 1855. The parachutist's rip cord (1906) originally was a device in ballooning to open a panel and release the hot air (1868, also ripping-cord).
Hence rip tide (by 1862), which seems at first to have been applied to strong tidal flows, as in the Pacific Northwest. An 1896 letter from Alaska, published in a California newspaper, describes a rip tide as "a rapid tide against a strong wind, producing choppy seas and an undercurrent, which renders a small boat unmanageable." By 1907, with the rise in popularity of ocean bathing, it came to be applied to dangerous intermittent strong currents flowing straight out from shore and can drag even strong swimmers to death by drowning. For this, precisians prefer the more accurate rip current, introduced for the purpose in 1936, but rip tide remains the popular term.
"thing of little value," 1815, earlier "inferior or worn-out horse" (1778, though OED regards this earlier appearance as "prob. accidental"), a word of uncertain origin, perhaps altered from slang rep "man of loose character; vicious, reckless and worthless person" (1747), which itself is of obscure origin, perhaps short for reprobate (n.). But also compare demi-rep "woman of dubious virtue" (1749, the second element said to be short for reputation).