1660s, "to shoot too low," from under + shoot (v.). In reference to aircraft or pilots, recorded from 1918. Undershot as a type of water wheel is recorded from c. 1600.
Entries linking to undershoot
under prep., adv.
Old English under (prep.) "beneath, among, before, in the presence of, in subjection to, under the rule of, by means of," also, as an adverb, "beneath, below, underneath," expressing position with reference to that which is above, from Proto-Germanic *under- (source also of Old Frisian under, Dutch onder, Old High German untar, German unter, Old Norse undir, Gothic undar), from PIE *ndher- "under" (source also of Sanskrit adhah "below;" Avestan athara- "lower;" Latin infernus "lower," infra "below").
Productive as a prefix in Old English, as in German and Scandinavian (often forming words modeled on Latin ones in sub-). Notion of "inferior in rank, position, etc." was present in Old English. With reference to standards, "less than in age, price, value," etc., late 14c. As an adjective, "lower in position; lower in rank or degree" from 13c. Also used in Old English as a preposition meaning "between, among," as still in under these circumstances, etc. (though this may be an entirely separate root; see understand).
Under the weather "indisposed" is from 1810. Under the table is from 1913 in the sense of "very drunk," 1940s in sense of "illegal" (under-board "dishonest" is from c. 1600). To keep something under (one's) hat "secret" is from 1885; to have something under (one's) nose "in plain sight" is from 1540s; to speak under (one's) breath "in a low voice" is attested from 1832.
shoot v.
Middle English sheten "hasten from place to place; move swiftly; thrust forward; discharge a missile, send an arrow from a bow," from Old English sceotan (class II strong verb; past tense sceat, past participle scoten), "dart forth, go swiftly and suddenly," also "discharge (a missile or weapon);" also, of a person, "go suddenly from place to place;" also transitive "send out or forth with sudden or violent motion; put forth or extend in any direction; strike with anything shot."
This is from Proto-Germanic *skeutanan (source also of Old Saxon skiotan, Old Norse skjota "to shoot with (a weapon); shoot, launch, push, shove quickly," Old Frisian skiata, Middle Dutch skieten, Dutch schieten, Old High German skiozan, German schießen), often said to be from PIE root *skeud- "to shoot, chase, throw," but Boutkan gives it no IE etymology.
The sense of "dart along" (as pain through the nerves or a meteor in the sky) is by late 13c.; that of "come forth" (as a plant) is by late 15c. As "increase rapidly, grow quickly" by 1530s (often with up (adv.)). By 1690s as "be emitted in rays or flashes" (as light is); by 1530s in weaving, "variegate by interspersing colors."
The general sports sense of "kick, hit, throw etc. toward the goal" is by 1874. In reference to pool playing, by 1926. The meaning "strive (for)" is by 1967, American English. The sense of "descend (a river) quickly" is from 1610s. The slang meaning "to inject by means of a hypodermic needle" is attested by 1914 among addicts. The meaning "to photograph" (especially a movie) is from 1890.
As an interjection, an arbitrary euphemistic alteration of shit, it is recorded by 1934.
Shoot the breeze "chat" is attested by 1938 (as shooting the breeze), perhaps originally U.S. military slang. Shoot to kill is attested from 1867. Slang shoot the cat "vomit" is from 1785.
To shoot the moon formerly meant "depart by night with ones goods to escape back rent" (c. 1823).
O, 'tis cash makes such crowds to the gin shops roam,
And 'tis cash often causes a rumpus at home ;
'Tis when short of cash people oft shoot the moon ;
And 'tis cash always keeps our pipes in tune.
Cash! cash! &c.
["The Melodist and Mirthful Olio, An Elegant Collection of the Most Popular Songs," vol. IV, London, 1829]
Shoot against the moon was used by Massinger (1634) as a figure of an impossible attempt.