meet

「多義語」とも言えますが、意味の根っこには統一的なイメージがあります。
１．定番
In the last century we humans have so vastly expanded our use of water to meet the needs of industry, agriculture, and a rapidly increasing population that now, after thousands of years in which water has been plentiful and virtually free, its scarcity threatens the supply of food, human health, and global ecosystems.（京都府立大）

２．バリエーション
The thrust of the article was that we need not feel we are helpless if disease tries to tear away at our bodies, and that we can have greater confidence in the reality of a healing system that is beautifully designed to meet most of its problems.(東邦大）

３．おまけ
...a romantic affair could meet with an obstacle. （愛知教育大）

４．定番＆基本
The local education board has also set up a counseling desk to meet needs varying from translating school memos and report cards to parents, to sending counselors to schools to meet students, parents and teachers. (愛知教育大学)

５．昔は受験問題の定番だった。
We're having trouble making both ends meet.

広い意味で「出会う」ですが、単に「出会う」だけではなく、「中身」も問題になるということでしょうか。まとめて言えば「出会って、かつ対応する、あるいは引き受ける」という意味合いです。