In a given model thare is
1.one to many relationship(identifying) between Project and Task.
2.one to many relationship(non Identifying) between Task and Assignments.
3. one to many relationship(non Identifying) between Resource and Assignments.
Surprising to me thare is no relationship shown between project and Assignments in datamodel diagram.But Assignment entity has Proj_id as part of primary key.
Is Proj_id in Assignments entity came due to relation with tasks and resource entity.
Resource appears to be independent of Project according to your relationships, but not according to the primary key of Resource - or did you omit a relationship between them by mistake?
Since the primary key of Task is (Proj_id, Task_id) then it follows that the Assignment table must also have those columns for its foreign key to Task.
Assignment represents the assignment of a Resource to a Task on a Project. If a particular Resource can only be assigned to a particular Task once, then there should be a primary/unique key on Assignment(Proj_id,Task_id,Resource_id). The PK shown uses a combination of Proj_id and a surrogate key called Assn_uid, which may be correct but does not enforce uniqueness of Resource/Task assignments.
So to answer your specific question, proj_id is in the Assignment table because it is part of the foreign key to Task.