It is told in one of the answers that the horizontal velocity stays at 4.0 m/s after the ball bounces from the plate.
Why is it still at 4.0m/s, isn't there friction or is it neglected for the sake of simplicity?
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The assumption is that there is no friction. In that case the horizontal component of velocity would remain same. In case of friction,there would be an impulse dure to friction acting on ball($=\mu J $where J is normal impulse) in left direction tangential to surface which would reduce horizontal velocity of ball