"I'm wondering what is this feeling."
Translation:Je me demande quel est ce sentiment.
"Is" isn't a preposition, it's a verb. There's no rule in English preventing a sentence from ending in "is". Even the "rule" that a sentence shouldn't end in a preposition isn't really a grammatical rule, it's just a stylistic choice. There's nothing grammatically wrong with ending a sentence with a preposition, it just makes the sentence sound less formal in some contexts.
I definitely agree that the given wording of the English sentence in this exercise is very unnatural sounding though.
"Quel" is used when there's a restricted set of options for what "quel" refers to, in this case the set of possible human feelings. "Ce qui" is used when there's no such restriction. For example, "Je me demande ce qui se passe" = "I wonder what is happening". In this case, "what" could be any event, without any kind of restrictions, so "ce qui" should be used and not "quel".
One way to check which to use is to consider whether it makes sense to replace "what" with "which" in the English sentence. If you can make the replacement and the sentence still makes sense without requiring additional context, "quel" is most likely the right option to use. Otherwise, if the sentence doesn't make sense anymore, it should be "ce qui".
We can apply this test to this exercise, though first let's reword the English sentence to be more natural: "I'm wondering what feeling this is." If you replace "what" with "which", it becomes "I'm wondering which feeling this is." The sentence still makes sense, and so "quel" is the right option.
We can also apply this test to the example I gave above: "I wonder what is happening." If you replace "what" with "which", it becomes "I wonder which is happening." Without additional context, this sentence doesn't make sense anymore, so "ce qui" is the right option.
I'll take issue with that! Yes you can. “Is” is just a verb. (Specifically, the 3rd person present tense of the verb “to be.”) There are no rules, and never have been rules, against ending sentences with verbs. We do it all the time. “Each week, my sister jogs.” “What are we going to eat?” “Where did everyone go?”
I think people get confused with “is” because it’s a “short word” and therefore feels like it should be governed by rules about prepositions like “in.” At one time it was generally believed that formal writing should avoid ending sentences with prepositions. Those rules are considered old-fashioned today and are not really enforced by any editors or style guides.
But regardless of that, “is” is not a preposition, just a regular verb, and can go anywhere in the sentence that makes sense. (All of the above sensible comments made by Ian Nicholson, a writer, editor and copy editor)