A ball rolls along a smooth horizontal floor at 10 m/s, then starts up a 20 degree ramp. How high does it go before rolling back?

If we neglect friction then only mgsin20 lower the speed of the ball

ma=mgsin20

a=gsin20=3.4 m/s^2

of course we insert it next formula with a negative because the speed decreases

v^2-v0^2=2ah

100-0=6.8h

h=100/6.8=14.7 m