How much force does it take to send a 200lbs object flying?

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Zeromaru
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To continue the title "How much force does it take to send a 200lbs object flying hundreds of miles?"

Anyway, I'm new here and amn't very good at physics but I really need an answer to this question and haven't been able to figure it out by myself. I'm sorry if it's a very stupid question, but as I've said, I'm not very good at this kind of stuff.
 
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I will need to ask you what you mean by "flying hundreds of miles". Are you looking for a certain height based on something like an explosion or someone swinging a sledgehammer and so on.
 
If you ignore air resistance then firing the object up at an angle of 45 degrees gives maximum range.

You can write two equations, one describing the vertical motion and one describing the horizontal motion. The flight time is obviously the same in both cases so these equations can be solved to find the velocity at which it would have to leave the ramp/ground/launcher in order to go "hundreds of miles".

Then what you do next depends on the launching method. If you are considering something like a navy aircraft carrier steam catapult or rail gun you could work out what acceleration was required to accelerate the object from zero to the required launch velocity over the length of the catapult. Then knowing the acceleration required you could apply one of Mr Newtons equations find the force required.