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The moon isn't at escape velocity either (source: It's still there).
Doesn't really change the numbers probably, but you'd need a little less than 11.2 km/s to reach the moon.
Wrong, that is not how orbital mechanics work. The moon IS below escape velocity, but it's orthogonal to the force of gravity. It also has a 240000 mile head start on getting away, yet it's STILL not escaping while traveling over 1km/s.
Shooting a bullet straight up, you would have to shoot faster than escape velocity for it to even reach the moon when using simple ballistic calculations.
There is A LOT of energy in those thousands upon thousands of miles.