I can't figure out how to upload the diagram so I'll do my best to explain it: the hoop is drawn with a horizontal line through the center, theta is the angle of the velocity vector above that dotted line. Hope that helps, sorry.
U1 = -GMm/r
K1 = (1/2)mvi^2
U2 = as r approaches infinity, U2 approaches zero
K2 = (1/2)mvf^2
(1/2)mvi^2 - GMm/r = (1/2)mvf^2 + 0
vi = √(vf^2 + (2GMm)/r) = √(250,000 + 2(6.7 E-11)(6 E23)/3400) = 153776.815
But that is not the correct answer, can anybody see my mistake/misunderstanding?
Based on this, I ruled out all of the answer choices that contained E, and found that the correct answer is "A, C, D", but I still don't fully understand C.
This has never been covered in my lecture class before, and I can't find anything useful in my textbook. Considering I'm completely unfamiliar with this verbiage, I figured maybe if I google definitions of these terms I would be able to figure it out, but google doesn't have many definitions...