GIVEN:A 1.9 kg solid cylinder (radius = 0.20 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.85 m high and 5.0 m long.

I got total energy by multiplying mass x gravity x h
that answer is 16.

I'm having a hard time finding rotational and translational kinetic energy.
For solid cylinder I know I=(1/2)MR^2
So I plug that into the equation and solve for velocity.
mgh=(1/2)mv^2+(1/2)((1/2)MR^2) (v^2/r^2)
w=(v^2/r^2)
So when I solve for v I get 4.6?
Is this right because I know this must be right to get Rotational.
Rot-KE=(1/4mv^2)

I could be way off. Any help is appreciated!

GIVEN:A 1.9 kg solid cylinder (radius = 0.20 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.85 m high and 5.0 m long.

I got total energy by multiplying mass x gravity x h
that answer is 16.

I'm having a hard time finding rotational and translational kinetic energy.
For solid cylinder I know I=(1/2)MR^2
So I plug that into the equation and solve for velocity.
mgh=(1/2)mv^2+(1/2)((1/2)MR^2) (v^2/r^2)
w=(v^2/r^2)


So far so good. But I don't see how you got v = 4.6. This collapses to:

mgh = 1/2 mv^2 + 1/4mv^2

Rearrange:
v^2 = 4gh/3 = 4(9.8)(0.85)/3 = 11.1 m^2/s^2
v = 3.33 m/s

That is where I messed up. I tried to multiply both side by 2 to get rid of (1/2)s.
When I set it up your way I got it right.

Thanks!