To simplify we can treat the wire as perfectly taut.
This allows the rope to exert a force on the tight rope walker (TRW)
Also for simplicity imagine the TRW as a solid body with a solid body pole that can be rotated about an axis parallel to the rope at a fixed location relative to the TRW.
Now, if the TRW is tipping clockwise their center of gravity will be to the right of the rope and moment created by gravity will add clockwise momentum. Similarly, if the TRW is tipping counter-clockwise gravity will add anti-clockwise momentum.
So the angular position of the TRW determines if clockwise rotational momentum is added or subtracted from the TRW+pole system. This angular position is determined by integrating rotational momentum of the TRW (divided by the moment of inertia) The amount of rotational momentum the TRW has can be modified by transferring momentum to and from the pole. While this doesn't directly affect the TRW+pole system's rotational momentum, it allows the TRW to control their angle, which in turn will affect the momentum of the system.
So if the TRW has too much clockwise momentum, and wants to move back to equilibrium, they can transfer a lot of clockwise momentum to the pole to temporarily tip themselves in the counterclockwise direction. If they tip far enough, then gravity will be eating away at the extra clockwise momentum, and the TRW can then take back some of the momentum given to the pole to bring themselves back to a neutral angle.
The drag force on an American football is in the range of a coefficient of .05 to .06. If the football is spinning the drag is slightly less.
The drag on a FIFA soccer ball is a coefficient of .25.
The football should travel further. The diameter of an NFL football is about 17.3 centimeters. The diameter of a FIFA soccer ball is roughly 22 centimeters. The greater cross sectional area of the soccer ball creates a thicker wake and more drag, as Sebastian Riese points out in his comment.
The chief difference between the balls, which produces less drag on the NFL football, is the shape. The NFL football's wake is significantly thinner than the soccer ball's, to a great extent because of the shape of the ball. The hulls of ships, for example, are designed like a football's shape below the water line toward the stern in order to allow a more laminar flow as the boundary layer separates from the back of the hull. Laminar flow creates a thinner wake which produces less turbulent viscous drag.
Best Answer
When you look at this video you can see that the lower leg seems to maintain a constant velocity. This is probably partially due to the higher total mass of the leg compared to the ball. The ball leaves the foot at a higher velocity. This due to the deformation of the foot and the ball. This deformation is caused by acceleration (initial velocity difference). When the ball tries to return to its original spherical shape, it will push against the foot, which pushes back and accelerates the ball.
Now if the initial velocity difference would be bigger, due to the ball moving towards you, the deformation will be bigger. Assuming that the leg still can maintain roughly a constant velocity, this means that the ball will be accelerated for longer and thus have a higher velocity.
And other way to look at this is that the ball bounces of a wall. However in this case the wall is moving. Relative to the wall the ball reverses its velocity normal to the wall, but with a slightly lower amplitude due to inelastic collision. But this means that if the ball initially is moving faster towards the wall the ball will move away from the wall faster. This can be done by moving the wall faster (kicking with a higher speed) or by increasing the incoming velocity of the ball.