Fortunately I posted an Answer before your question was put On Hold. This allowed me to develop it further without competition (or interest) from anyone else. The challenge of the question is its own reward : I do not feel robbed without the bounty you would like to offer, particularly since I had no competition.
My disappointment with the On Hold decision is that it prevents any alternative solutions and contrary views from being explored, such as M Barbosa's vector approach. Good Answers emerge from healthy debate. The Up Votes show that it is a popular and slightly controversial question (perhaps Game of Thrones fans like you), so I would have expected at least 2 more Answers.
But the consensus even among those who did not Vote to Close seems to be that the question is "off topic". Personally I disagree. It is Applied Mathematics, and requires calculations of speed, time and distance - but so is any question on kinematics or projectile motion, which are "on topic".
Moreover, the broader context of the question requires the development of an appropriate mathematical model, instead of being handed one on a plate. This involves deciding which factors are the most significant, how they can be represented mathematically, and what approximations to make. Seeing the different approaches and solutions that working physicists with different backgrounds bring to modelling the same situation can be very instructive for everyone.
It would be helpful if those who did Vote to Close, or up-voted the "off topic" comment, were more willing to discuss where they think the boundary lies between what is on- and off-topic. Or at least provided Answers to this Meta question. Merely pointing you to the Help Center is not very helpful!
Cynically, I think M Barbosa is right : If you had replaced the Game of Thrones context with an artificial one using a few physics concepts - eg neutrinos being fired at neutrons which can somehow be steered left and right (you don't need to say how, just call it a Thought Experiment) - then I think it would never have been put On Hold! My own Answer goes a little in this direction by mentioning "collision cross-section."
Seriously, you might include gravity in your model (which is already there in the GoT scenario), making it explicitly a question about projectile motion. You might also consider replacing the Newtonian Mechanics tag (which is not strictly applicable) with Applied Physics. Finally, flag the question for Moderator attention, explaining what changes you've made and why you think it is now "on topic".
But I have no evidence that this would be successful. I have appealed against the closure of several questions, without any success.
UPDATE
Since posting the above Answer, I now appreciate why the question is deemed off-topic by those who voted to close it. A change of terminology, or even focussing on projectile motion, would not have altered the decision, for the reasons given by ACuriousMind in his Answer. I think such problem-solving questions should not be off-topic for the site, but I agree that, as a matter of fact, according to the current site policy this one is off-topic.