It is not uncommon to see people writing “down the shoot” when they mean “down the chute.”
A chute is a sloping channel things move down along. It comes from the French word for “to fall.”
But if you are a shipper of Chinese groceries you could shoot cans of bamboo shoots down a chute to the loading dock.
“Chute” is also short for “parachute,” but people rarely misspell it in that sense.