long shot (n.)

Old English lang "having a great linear extent, that extends considerably from end to end; tall; lasting," from Proto-Germanic *langa- (source also of Old Frisian and Old Saxon lang, Old High German and German lang, Old Norse langr, Middle Dutch lanc, Dutch lang, Gothic laggs "long").

The Germanic words perhaps are from PIE *dlonghos- (source also of Latin longus "long, extended; further; of long duration; distant, remote," Old Persian darga-, Persian dirang, Sanskrit dirghah "long"), from root *del- (1) "long" (source also of Greek dolikhos "long," endelekhes "perpetual"). Latin longus (source of prolong, elongate, longitude, etc.) thus is probably cognate with, but not the source of, the Germanic words. The word illustrates the Old English tendency for short "a" to become short "o" before -n- (also retained in bond/band and West Midlands dialectal lond from land and hond from hand).

Also in Old English in reference to time, "drawn out in duration," with overtones of "serious." The old sense of "tall" now appears to be dialectal only, or obsolete. For long "during a long time" is from c. 1300. To be long on something, "have a lot" of it, is from 1900, American English slang. A long vowel (c. 1000) originally was pronounced for an extended time. Mathematical long division is from 1808. Sporting long ball is from 1744, originally in cricket. Long jump as a sporting event is attested from 1864. A long face, one drawn downward in expression of sadness or solemnity, is from 1786. Long in the tooth (1841 of persons) is from horses showing age by recession of gums (but not in this sense until 1870). Long knives, name Native Americans gave to white settlers (originally in Virginia/Kentucky) is from 1774, perhaps a reference to their swords. Long time no see, supposedly imitative of American Indian speech, is first recorded 1919 as Chinese English.

Middle English shot "a missile, arrow, dart" (senses now archaic or obsolete); "a swift movement, a gushing out," from Old English scot, sceot "a shot, a shooting, an act of shooting; that which is discharged in shooting, what is shot forth; darting, rapid motion."

This is from Proto-Germanic *skutan (source also of Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), from PIE root *skeud- "to shoot, chase, throw." The Old English noun is related to sceotan "to shoot." The meaning "discharge of a bow, missile," also is from related Old English gesceot.

The noun was extended to other projectiles (balls, bullets) by mid-15c. Especially "lead in small pellets, a small ball or pellet," a number of which are combined in one charge, which is attested by 1770 (shortened from earlier small shot, 1727).

The general sense of "an attempt to hit with a projectile" is by 1650s. Extended to sports (hockey, basketball, etc.) by 1772, originally in curling. It is attested by early 15c. as "range or distance of a missile in flight," hence "range" in general (c. 1600), as in earshot. 

Another original meaning, "payment" (perhaps literally "money thrown down") is preserved in scot-free; also see scot (n.). The notion of "throwing down" might have led to the meaning "a drink," first attested 1670s; the more precise meaning "small drink of straight liquor" is by 1928.

The sense of "hypodermic injection" is attested from 1904; the figurative phrase shot in the arm "stimulant" is by 1922. The broad meaning "a try, an attempt" is by 1756; the sense of "remark meant to wound" is by 1841. The meaning "an expert in shooting with a firearm" is from 1780; the sense of "a rocket flight" is by 1934. The camera-view sense is by 1958.

To call the shots "control events, make decisions" is American English, 1922, perhaps from sport shooting. Shot in the dark "uninformed guess, random attempt" is by 1885. Big shot "important person" is from 1861. 

By the rude bridge that arched the flood,

   Their flag to April’s breeze unfurled,

Here once the embattled farmers stood

   And fired the shot heard round the world.

[Emerson, from "Concord Hymn"]