A 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 a ball B of same mass which is placed on the top of a pole. At 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 â€‹forward direction. If it is known that the height at which the ball is placed is the maximum height that the initial projectile of ball A would have travelled , 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**:

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

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