The use of the prepositional phrase in this sentence is adjective, because it is part of the noun phrase - the basketball on the roof. If it weren't a part of the phrase, it would probably be an adverb, but this way, it is not.
We are given the sentence, "The basketball on the roof is Jerod's". THe prepositional phrase is "on the roof". The phrase describes the basketball which is a noun. A word or group of words that describes a noun is called an adjective.
