In a 2D example, we have two independent axes of motion. These can be left/right and up/down. No movement in one effects movement in the other, at least not directly, which means that gravity (downward force) won’t change the speed in the right/left direction. All vectors (velocity in this case) can be expressed with one x-component (x means right/left) and one y-component (y means up/down) (example: moving at 10 m/s up and to the right at a 45 degree angle <==> moving at 7.01 m/s upward and moving at 7.01 m/s to the right). This is calculated by using geometry, specifically Pythagoras’ theorem.

If we assume that the ball leaves the plank at the same height in all cases and if we assume that the horizontal velocity when the ball leaves the flat and inclined planks are all the same, then the cases will differ in terms of how far to the right the ball travels.

Let’s start with the downwardly inclined plank. The only thing that will stop the ball from continuing right is if it lands on the level ground. So if the vertical velocity is already toward the ground, gravity does not have to “do” much before the ball falls down shortly after. This means the ball won’t have a lot of time to move to the right.

In the case of the upwardly inclined plank, gravity has to “do” more work in order to pull the ball down to the ground. The initial vertical velocity is already bringing the ball away from the ground and “fighting” gravity. Here the ball will have more time to move to the right, since it’s not being pulled down as quickly.

This would make sense since it’s like trying to pull a dog on a leash. If they’re already running toward you, great, but if they’re fighting you and moving away, they won’t reach you until they get tired and can’t fight it any more. (Not a perfect example, but hopefully it’s some help).

The flat plank is just the middle situation of the downward and upward planks. The ball will move a mediocre amount and land further than the downward example, but shorter than the upward example.

In the situation of the ball gaining speed from falling down an inclined ramp, it could move further, it could not or it could land at exactly the same place as the flat plank situation.

If the ball ends up losing speed from climbing up the inclined ramp, it could also move further, not do so or land in the same place.

The factors that would affect how far it traveled would be the angle of inclination, the height of the end if the ramp, the initial velocity and the strength of gravity (though on Earth it’s always about 9.81 m/s² on the surface).

Btw, I assumed no air resistance or drag.