...this is a SPECTACULARLY BAD mistake on his part.

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OK. I dropped a factor of 2 somehow. If that's "SPECTACULAR" you guys are awfully easy to entertain. There's a lot easier way to do the problem than all the work you went through, by the way.

Simply equate potential energy at the start to kinetic energy at the finish.

mgh=0.5mv^2. Solving for v you get v=sqrt(2gh).

For h=52.78 m, v=32.16 m/s.

I probably divided by 2 instead of multiplying by 2 inside the radical. I probably shouldn't do these things in my head. Let's make a deal. I'll concede when I'm wrong and you concede when you're wrong. That could lead to civil discussions.

This originated as a quick little side calculation...a little too quick apparently. It has zero bearing on the substance of the horizontal ejection issue.