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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