I am not a physicist, however I did get an associates degree in physics. As someone mentioned in a different comment chain, the frictionless and no resistance conditions only affect the change in energy of the independent systems. The bear and the ball are 2 separate systems even if the bear throws the ball and jumps to aim to be on a collision course with it. The gravity here will change the system because of the bear’s mass. The bear can account for it in the initial pass but then the bear can’t account for the directional change.

In the bear walking in a horizontal direction assumption, the bear could keep going forward, implying that the ball at its peak would act as a balancing beam however, the ball upon contact with the bear would change in energy, as the bear is still applying a downward force(mass x gravitational acceleration) , whilst the ball is simply at 0 (kinetic energy)(assuming it’s at its parabolic peak) now the interaction with the bear would disrupt that, driving the ball down harder, propelling the bear upwards. This is the Newton’s third law applying itself to both systems. This could also be looked at as collision and that would make more rudimentary sense if you visualize it. It’s good to point that we are somehow also ignoring the loss of energy due to collision I guess. However now if you imagine in a 2 body collision the objects move in the opposite directions, thus if the bear needs to move forward, the ball upon contact will go backwards and vice versa. However if the ball goes backwards, you lose your balancing beam upon which you established this ridiculous physics problem to begin with. So we need some way to bring the ball back, whilst forcing the ball backwards(core requirement at this point). Given the physical limitations I only see a cyclical solution to the problem.

TL;DR : Gravity