Alittle boy sitting on the floor tosses a ball in such a way that it reaches the level of a tabletop several meters away, moving horizontally, and rolls across the tabletop at constant speed if friction with the air and the tabletop can be ignored, with what speed does the ball roll across the tabletop?

Let
u = the horizontal component of the launch velocity,
v = the vertical component of the launch velocity.

Because air resistance is ignored, the horizontal velocity remains unchanged.
The vertical velocity diminishes to zero due to gravitational acceleration.
Therefore the ball rolls across the tabletop with horizontal velocity, u.

The speed of the ball remains constant at u on the tabletop (see the diagram shown below) because rolling friction is ignored.