Old English hær "hair, a hair," from Proto-Germanic *hēran (source also of Old Saxon, Old Norse, Old High German har, Old Frisian her, Dutch and German haar "hair"), perhaps from PIE *ghers- "to stand out, to bristle, rise to a point" (source also of Lithuanian šerys "bristle;" see horror).
Spelling influenced by Old Norse har and Old English haire "haircloth," from Old French haire, from Frankish *harja or some other Germanic source (see above). Hair-dye is from 1803. To let one's hair down "become familiar" is first recorded 1850. Homeopathic phrase hair of the dog (that bit you), remedy from the same thing that caused the malady, especially a drink on the morning after a debauch, 1540s in English, is in Pliny.
ball n.1
"round object, compact spherical body," also "a ball used in a game," c. 1200, probably from an unrecorded Old English *beal, *beall (evidenced by the diminutive bealluc "testicle"), or from cognate Old Norse bollr "ball," from Proto-Germanic *balluz (source also of Dutch bal, Flemish bal, Old High German ballo, German Ball), from PIE root *bhel- (2) "to blow, swell."
The meaning "testicle" is from early 14c. (compare ballocks). Ball of the foot is from mid-14c. The meaning "rounded missile used in warfare" is from late 14c.
The meaning "a game played with a ball" is from mid-14c. The baseball sense of "pitch that does not cross the plate within the strike zone" is by 1889, probably short for high ball, low ball, etc.
Ball-point pen is by 1946. Ball of fire when first recorded in 1821 referred to "a glass of brandy;" as "spectacularly successful striver" it is attested from c. 1900. Many phrases are from sports: To have the ball "hold the advantage" is from c. 1400. To be on the ball is from 1912; to keep (one's) eye on the ball in the figurative sense is by 1907, probably ultimately on golf, where it was oft-repeated advice. Figurative use of ball in (someone's) court is by 1956, from tennis.
The head must necessarily be steady, for it is most important that you should keep your eye fixedly on the ball from the moment that the club-head is lifted from the ground until the ball is actually struck. "Keep your eye on the ball," should be your companion text to "Slow back." [Horace G. Hutchinson, "Hints on the Game of Golf," 1886]
Once a meeting is over, someone will be expected to do something. Make sure it is someone else. This is known as keeping the ball in their court. [Shepherd Mead, "How to Get Rich in TV Without Really Trying," 1956]