Can adjectives be placed in front of verbs, e.g. “The duck was busy diving for food”?
The positional nature of English grammar gives your two sentences different structures in spite of the similarity of their wording. To see this, let's look at a similar pair of sentences that have the same structure:
1a. The busy duck was diving for food.
2a. The duck was diving busily for food.
(Ignore the slightly awkward placement of "busily" in the second sentence.)
The basic structure of both sentences is
Subject - Verb - Adverbial Prepositional Phrase
Subject = "duck"
Verb (past progressive tense) = "was diving"
Prepositional Phrase (of purpose) = "for food"
The difference, of course, is that the first sentence has at attributive adjective ("busy") modifying "duck," and the second has an adverb of manner ("busily") modifying "was diving." The different modifiers, however, don't affect the basic structure.
But things are different for the original first sentence:
- The duck was busy diving for food.
Now the structure of the sentence is
Subject - Copulative Verb - Predicate Adjective - [Present Participle Phrase]
Subject = "the duck"
Copulative Verb (simple past tense) = "was"
Predicate Adjective = "busy"
[Present Participle Phrase] = "diving for food"
The Present Participle Phrase is in brackets because I'm delaying describing it's function in the sentence, but in any case, the participle "diving" isn't part of the verb as in sentence 1a.
So what is it? You may decide that it's an adverbial phrase of purpose modifying the verb telling us why the duck was what it was, or you may decide that it's a nominative absolute, associated with but independent of the subject-verb combination.
Both of the sentences are correct.
Can an adjective be placed in front of a verb?
The answer is yes. Consider some examples given below:
It was such a delight to see him so happy swimming in the pool, with his own audience of doting adoring people.
[from the book A Mummy's New World by Deborah Harrow]
I was playing out in the backyard, and when I came into the kitchen, Mom was busy baking cookies.
[from the book Happiness Pursued by Shubel Hudson Owen]
The congregation had come out half an hour ago, and she felt lonely walking in the dark toward the light.
[from the book The Complete Stories, Volume 1 by Morley Callaghan]
About the second sentence: "The duck was busily diving for food."
This is correct, too. An adverb ('busily' in this sentence) can be either before or after the verb. You can refer to this post which talks about it:
Should an adverb go before or after a verb?
'Busy', in the first sentence, seems to modify 'duck' rather than 'diving' - as in a declaration of the duck's status.
Whereas 'busily' unambiguously refers to 'diving' in the second sentence.