# Ok, you go up but how far?

Take a solid cylinder of radius $$R$$ , roll it with angular velocity $$\omega_{0}$$ and carefully keep it on an inclined plane having inclination $$\theta$$ , and coefficient of kinetic friction $$\mu_{k}$$ , such that $$\mu_{k} > \tan \theta$$. Find the maximum height attained by the cylinder above the initial position in $$mm$$ to the nearest integer

Details and Assumptions

• $$\omega_{0} = 50 rad s^{-1}$$
• $$R = 25cm$$
• $$\mu_{k} = \frac{1}{3}$$
• $$\tan \theta = \frac{1}{4}$$
• $$g=9.8 m/s^2$$
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