IPA: /əˈpɒsɪtli/
KK: /əˈpɑːsɪtli/
In a way that is appropriate or suitable for the situation.
She responded appositely to the question, showing her understanding of the topic.
Appositely is formed from "apposite" (from Latin "appositus", meaning placed near or appropriate) and the suffix "-ly" (meaning in a manner of). The word "appositely" means in a manner that is appropriate or suitable to the situation.
Think of something being 'placed near' or 'appropriate' — that's what appositely means, as it describes doing something in an appropriate manner.