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The escape velocity for the Earth is 11.2 km/s. If you shoot a cannonball upward at that speed, it'll have enough energy to completely leave Earth and never come back.
Would shooting it at that speed work? Wouldn’t it need to maintain that speed?
From wiki.
assuming:
Ignoring atmospheric drag, it would.
Yes, but there is air resistance. And as mentioned in the question, you can use moon to slingshot the object. Also, I guess it is better to accelerate during the ascendancy, probably because of the friction, otherwise rockets would be replaced with cannons.
Well, they're not exactly using cannons, but we do have SpinLaunch. It comes with a lot of impractical limitations, but it's still pretty cool.