# You shall not spin!

A uniform rod of length $$2$$ m and mass $$16$$ kg is thrown vertically from the ground, such that the top of the rod reaches a height of $$h$$ (from the ground). At the moment that it reaches its apex, a ball of mass $$3$$ kg traveling horizontally hits the top of the rod with a velocity of $$10$$ ms$$^{-1}$$ and binds to the very end of the rod. The rod now starts to spin. It perfectly completes one full rotation and then hits the ground.

Find $$h$$ in meters.

Details and Assumptions

• The ball is a point particle.
• The rod has no cross-sectional area.
• There is no air friction.
• A complete rotation indicates that after rotating through an angle, the ball-rod system is vertical again, with the ball at the top.
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