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**1. A solid uniform cylinder of mass M and Radius is projected up an incline of angle Ө. It rolls without slipping from an initial speed V๐ of the center of mass. What distance s does the center of cylinder travel before it starts to fall back?**

**2. I=½MR², V²=V๐²+2as, F=ma, a=R²α ...**

**3. MgsinӨ+f=ma=mR²α**, f=Iα/R

0²=V๐²-2as , I=I=½MR² , a=2gsinӨ

s=V๐²/4gsinӨ

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But the answer page of the book says s= (3V๐²/4g) sinӨ [exactly as it's written---Prob. 9/67 PHYSICS for.... 3rd Edition; Fishbane-Gasiorowich-Thornton]

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I've found another solution from another book which goes with the conservation of the energy:

½MV๐²+½Iω๐²=MgH , H=SsinӨ

For a solid uniform cylinder, rotational kinetic energy is 1/3th of total energy and therefore:

3/2(½MV๐²)=MgSsinӨ, s=3V๐²/4gsinӨ

Which of us is correct????