why do ballistic trajectories have such a distinctive arc?

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what i mean is that when say, an artillery shell is fired, or a piece of debris from an explosion is launched, it goes up and away at an almost 45 degree angle until its upwards momentum is no longer sufficient to fight gravity before dropping pretty much straight down. second, given the angle of impact on the ground, could you calculate backwards from there the initial velocity and launch site of the projectile?

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Anonymous 0 Comments

Any unpowered object flying through the air will travel with the combination of 2 formulas: the vertical axis, which is made up of how much velocity it has vertically subtracted by the acceleration of gravity; and the horizontal axis, which is made up of how much velocity it has horizontally. If we ignore the real world things (like air resistance) this will always create a parabola.

So because parabolas are very well studied shapes (especially with calculus), if we know the shape of one part of it and the acceleration it has been going through (aka gravity, so yeah we know it) we can backtrack the shape of it at any other part.

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