The Talmud states that if someone threw something and it landed in the hand of another, the thrower is liable. R. Avin, citing R. Yochanan, notes that if the second person stood still and caught it, the thrower is liable; if the second person moved and caught it, the thrower is exempt. Some acharonim (as cited by R. Shmuel Rothschild, in the journal Kol Torah, issue 59, p. 11 in Kovetz “Simchat HaTorah”) ask why this different than the situation of one placing a pot of food on the fire on Shabbat and another stirs the food, in which case both parties are liable (see Beitzah 34a).

The Avnei Nezer (Responsa, O.C., 128) asserts that the two cases are not comparable. In the case of the catch, the putting of the object to rest (hanachah) was not done at all by the thrower; in fact, left alone, it would have been placed down elsewhere. In the case of cooking, the total effect of the cooking was a joint effort of the one who placed the food on the fire and the one who stirred it.

The Afikei Yam (II, 4:3) discusses why the cooking situation is not one of “two who have done it” which is normally exempt. He suggests that this principle is only applicable when, in order to assign liability, the actions of both individuals must be combined. However, the stirrer could have performed his action on a pot that had been on the fire from before Shabbat, and thus has no dependency on the first one. He concludes, though, unsatisfied as to the liability of the first party, as the act of cooking only was completed through the action of the second.