Isn't the word "next" necessary here? Like, "go next".
To ask "where does the chute go next", would imply that there are multiple stops for the chute, which is most likely not the case here. However asking "where does the chute go" asks about the final destination of the chute; where it ends. Which is what he wants to know. Ex: A. Where does this cup go? B. Put it in the cupboard. Ex: I wonder where he will go.
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