入 means "enter", 口 means "mouth". 入口 means... "entrance". Actually for most kanji there is no single meaning. Some meanings might even have nothing in common with each other, because they've been based on ancient Chinese wordplay or something.
A vomitorium (any modern person associates that with vomiting, i.e., stuff coming out of your mouth) was the name for entrances in Roman amphitheatres.
(idiomatic) To exert maximum effort.
https://en.wiktionary.org/wiki/put_the_pedal_to_the_metal#En...
http://compling.hss.ntu.edu.sg/omw/cgi-bin/wn-gridx.cgi?usrn...
It's not that a land's-mouth is a crater, more like, mouth and opening are more synonymous in feeling in Japanese.