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

The figure below would help in understanding the situation:

**Details and Assumptions:**

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

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