The young girl with the long black hair fell from her bike yesterday in heavy rain.

Question

In these sentence where is the preposition?Is heavy rain is the preposition?

Answer 1

There are three prepositions in this sentence:

with

from

in

Each preposition has other words to complete its meaning; these word combinations make prepositional phrases.

with the long black hair
from her bike
in heavy rain

As you can see, the words "heavy rain" are part of the 3rd prepositional phrase, but are not the preposition itself.

Here is a long, but very complete, explanation about prepositions and their phrases -- and lots of examples:
http://grammar.ccc.commnet.edu/grammar/prepositions.htm