What is your difficulty? You are given an acceleration vector [itex]-g\vec{j}[/itex] and, I presume, you know that the velocity vector is the integral of that [itex]-gt\vec{j}+ \vec{v}(0)[/itex] where [itex]\vec{v}(0)[/itex] is the "initial velocity" vector. You are given that by being told it has "magnitude v at an angle [itex]\theta[/itex] to [itex]\vec{i}[/itex]". Do you know how to write such a vector at that angle? (Think about the lengths of the legs of a right triangle with hypotenus of length v and one angle [itex]\theta[/itex].)
Once you have [itex]\vec{v}(0)[/itex] add it to [itex]-gt\vec{j}[/itex] to get the velocity vector as a function of t and integrate again.