A solid cylinder rolls up an inclined plane of inclination θ with an initial velocity v. How far does the cylinder go up the plane?

Let the cylinder go up the plane upto a height h. Let M and R be the mass and radius of cylinder respectively. According to law of conservation of mechanical energy, we get            12Mv2+12Iω2 = Mgh (∵ For a solid cylinder, I = 12MR2)           12Mv2+14MR2ω2 = Mgh             12Mv2+14Mv2 = Mgh     (∵ v = Rω)             34Mv2 = Mgh              h = 3v24gLet s be distance travelled by the cylinder up the plane.       s=hSin θ=3v24gSin θ