I won't possibly throw like that, would I?

Ball AA of mass 1 kg1\text{ kg} is thrown at an angle of 45{45}^\circ with the horizontal with kinetic energy 50 J50\text{ J} such that it hits ball BB of the same mass placed on the top of a pole. In this collision, half of the kinetic energy of ball AA at that instant is transferred to ball B,B, causing ball BB to move in a forward direction. If it is known that the height at which ball BB was placed is the maximum height that the initial projectile of ball AA would have traveled, then find the distance of the final position of ball BB from the foot of the pole.

The figure below would help in understanding the situation:

Details and Assumptions:

  • Ball BB does not rebound after hitting the ground.
  • Air friction is negligible.
  • Take g=10 m/s2g=10\text{ m/s}^2 as the acceleration due to gravity.
  • Give your answer (in m\text{m}) to two decimal places.

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