Question

Two balls are thrown from the top of a tower of unknown height with same speed 10m/s

Answer 1

First, I think you meant, “when the velocities are parallel to each other”

I can’t think of an instance where the velocities would be at perpendicular, given the setup in the question.

I have been considering what happens to a ball when it it thrown horizontally from a tower of some height. The real question is, does the ball ever fall completely vertical, or does it continue in it’s horizontal path, decelerating of course, but never having the horizontal vector reach completely zero.

I am oing to say that the horizontal velocity will never reach zero. As the ball falls, the horizontal velocity will decay due to air resistance, but never (theoretically) reach zero. Since horizontal velocity must be zero for an object to fall vertically, the condition in your question will never occur.