A uniform solid cylinder rolls without slipping at $4.0\ \text{m/s}$ along a rough level floor. Ahead, the floor joins smoothly onto a ramp whose surface has no friction at all, as shown in the figure. The cylinder goes up the ramp, comes back down, and returns onto the rough floor. What is its velocity once it again rolls without slipping on the floor?

Fig. 1: A level rough floor on the left joins smoothly to a smooth ramp that rises to the right at about 25 degrees. A cylinder rolls on the floor towards the ramp, its centre moving to the right at v0 = 4.0 m/s while it spins clockwise.