Does "precipitation" have anything to do with "precipitous"?

Question

precipitation

1. the action or process of precipitating a substance from a solution.
2. rain, snow, sleet, or hail that falls to the ground.
3. archaic,the fact or quality of acting suddenly and rashly

It's a synonymous of drop I think;

While precipitous

1. dangerously high or steep:
2. (of an action) done suddenly and without careful consideration:

synonyms: steep · sheer · perpendicular · abrupt · sharp · vertical

Both give me a sense of abruptly and related to the "altitude", "vertical". So, it's of pure coincidence or they have something to do with each other? Say coming from a same root? Tried but found nothing related, So I thought I'd post. Apologies if it contains grammar mistakes and wrong use of words. Feel free to edit it.

Answer 1

Yes, the etymology is the same praecipitare:

precipitous (adj.)

• 1640s, "rash, headlong," from obsolete French precipiteux (16c.), from Vulgar Latin *praecipitosus, from praecipitare (see precipitation).

precipitation (n.):

• late 15c., "a casting down" (of the evil angels from heaven), also, in alchemy "separation of a solid substance from a solution," from Middle French precipitation (15c.) and directly from Latin praecipitationem (nominative praecipitatio) "act or fact of falling headlong, haste," noun of action from past participle stem of praecipitare "fall, be hasty," from praeceps "steep" (see precipice). Meaning "sudden haste" is c. 1500. Meaning "act of falling from a height" is attested from 1610s. Meteorological sense of "rain, snow, dew, etc." is from 1670s.

(Etymonline)