Avast ye, mateys!

This here be a follow up riddle, a sequel if ye will, to a previous puzzle that’s been hidin’ in these digital waters for a while now. It be a fine and simple ol’ challenge, that first one, and ye should be plunderin’ it before ye set sail on this new adventure. So hoist the sails and set a course for the original puzzle, then come back here for additional booty!

Follow Up Questions to the Original Puzzle

1. The survivors from the original puzzle developed teleportation technology! Instead of their ship having a constant integer velocity, they now instead have a fixed (but unknown!) computer program get_teleport_destination, that gets the day number as input (it gets 0 on the first day, 1 on the second, etc.) and generates arbitrary new (still integer) coordinates, once per day, and the ship instantaneously teleports to these new coordinates. As before, you don’t know the ship’s starting coordinates, and you are allowed one shot per day. To decide where to shoot, you must also use a computer program that will produce each day the coordinates to shoot at. Show that you can no longer guarantee the destruction of the ship.
2. You now learned that the ship is running the get_teleport_destination program on a single specific CPU, say an 80386 computer. Remember that you know that it takes no more than 24 hours to compute the coordinates. Produce a computer program that generates coordinates to shoot at, that will destroy the ship. For extra-credit, provide an upper bound on the number of days needed until the ship is destroyed and on the amount of computing power you’d need to guarantee destruction.

A hearty “thank ye” to Gemini, the digital parrot, for helpin’ me turn this olde post into pirate speak!