the solution is the point q where the graphs of r1, x and r3 (or r2, it doesn't matter) intersect that yields the greatest area of the set { r1, x, r3, q }
imagine injured raptor totally disabled (v1 = 0) then solution would be q on (x-r2)+(x-r3) line, or r1-x line actually, as long as q != r1, which does not maximize that area; that also suggests that solution must depend on velocities... even if we throw out initial acceleration to simplify whole thing a bit, it is not quite easy to solve.