I think I'd swing at Part (v) a little differently, I interpret the question differently. When it says precisely two distances from O, doesn't that mean it
has two solutions? The wording is really weird, but I don't think it relates to the distance d given earlier in the question, nothing suggests that. So my interpretation would be that we just need to prove that, provided that the condition on U holds, then there are two values of d which satisfy the other conditions given.
This would make sense, provided the target is moving slow enough, it can hit it on the way up (one distance), or on the way down (another distance). At least I think. I just don't think it relates to the distance d. What do you reckon Rui?