Yes, I had shown that
rbullet=rtarget⟺rA=rB i.e. that gravity is irrelevant and that it is necessary (and sufficient, but that's not important here) that
A,B collide in order for the bullet to hit the target.
Furthermore, by "cartesian trajectory", I meant the equation of motion that relates
x and
y and I presume this is what you meant by "actual trajectory". The trajectories of
A and
B (that is, of the particles of part (i))
are straight lines - this is immediate from the parametric forms of part (i) by eliminating
t (mentally or otherwise) and indeed what one expects if gravity does not influence the motion. So, for the bullet to hit the target, it is therefore necessary that these lines must intersect in the upper right quadrant. My conclusion follows.*
I must say this is
all in my explanation for the last part, and I felt this was the whole point of the question. I'm still unsure where you feel an issue lies.