This is a word problem that was given to my group as a project and the problem itself is rather lengthy so I will give the portions that are relevant to the problem.

The set up to the problem is that your group was studying for finals and suddenly you pass out and wake up on planet Xanthar. You meet a man named Victor Field at a Tavern and he tells you the only way to get back home is by using a catapult to launch the holy hand grenade of antioch into the castle of the evil wizard Div Curl.

1. The problem statement, all variables and given/known data

I am paraphrasing from the problem:

"[Victor Fields tells you that]...the perimeter of [Div Curl's] castle compound is impenetrable on the ground, surrounded by a 30 foot tall magic wall. He also says the forests surrounding the compound is surrounded by dragons, that patrol an area 1000 feet from the compound wall. (The compound is a circular compound with a radius of 1 mile). he hands you a copy of blueprints for a great catapult (from the ACME company), which can be used to launch the Holy Hand Grenade of Antioch. He tells you that the catapult fires its object with an elevation angle of 60 degrees and an initial speed of 2000 ft./sec. He also tells you that the catapult will not function unless it is on perfectly level ground and cannot be placed either above or below basic ground level of the magic forest. He hands you a book of matches and a copy of a book written in an obscure ancient XantHurian dialect. finally he hands you a bird in a cage which you immediately recognize to be an African Swallow. He also tells you that the atmospheric pressure on Xanthar behaves as it does on earth, with identical density but that the gravity near the castle operates radially from the center with the equation:

g(t)= (-2 + sint)i+ (-32 + cost)jft/sec^2 where t is in seconds.

He also tells you that the drag acceleration due to air resistance in the Xanthurian atmosphere is numerically equal to the velocity and you know this to be a vector equation."

2. Relevant equations

gravity =g(t)= (-2 + sint)i+ (-32 + cost)j

3. The attempt at a solution

My group used g(t) as our vector field.

Our goal is to find what distance away from the compound do you need to be able to fire the holy hand grenade of antioch into the compound.

That is how far we have gotten so far. We have worked on this problem for days and we still have not gotten it.

Our professor said that there are missing elements that we need to complete the problem and that we need to find what these elements are ourselves.

The issue is that we don't know what we are missing. If anyone can point us in the right direction then it will be a great help. We do not need the answer, we just need to know what we are missing. Thank you so much for any help!