The game engine applies friction (this is the term used in the statement, equivalent to “resistance” in your message) after the pods have moved, i.e. at the end of every turn. So:
Turn 1:
X speed during current turn = Old X speed + thrust = 0 + 88 = 88
X-coordinate = Old X-coordinate + speed = 4000 + 88 = 4088
X speed at the end of turn = “Old” X speed x 0.85 = 88 x 0.85 = 74
4088 and 74 are shown in turn 1 of the replay.
Turn 2:
X speed during current turn = Old X speed + thrust = 74 + 88 = 162
X-coordinate = Old X-coordinate + speed = 4088 + 162 = 4250
X speed at the end of turn = “Old” X speed x 0.85 = 162 x 0.85 = 137
4250 and 137 are shown in turn 2 in the replay.
Turn 3:
X speed during current turn = Old X speed + thrust = 137 + 88 = 225
X-coordinate = Old X-coordinate + speed = 4250 + 225 = 4475
X speed at the end of turn = “Old” X speed x 0.85 = 225 x 0.85 = 191
4475 and 191 are shown in turn 3 in the replay.
Hope this explanation helps you understand how the game engine works in this game.
If you still have questions on distance and angle as mentioned in your original post, please kindly explain your calculation using this replay too, and I will try to help you understand 
btw, code in this forum should be formatted using the </> button in the formatting toolbar 