The caber toss is a traditional Scottish sport that involves hurling a caber, which is essentially a large piece of a tree: a caber is a \(6~\mbox{m}\) long, \(80~\mbox{kg}\) tree trunk. Large strong people hurl these and the goal is to get the caber to land as far away as possible and rotate in the air, so what was the highest part of the trunk initially is actually the part that hits the gound first. See this clip to understand how the caber rotates.

It's HARD to do this. To see how hard, consider a perfectly vertical caber with one end on the ground. You then launch the caber vertically with some speed \(v_0\) and give it a rotation. What is the minimum kinetic energy **in Joules** you need to give the caber so that when it lands the caber is perfectly vertical again, but the OTHER end of the caber hits the ground?

**Details and assumptions**

- The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
- The caber can be modeled as a uniform rod.

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