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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Yes, you can and there are anti-artillery weapons systems based on this concept:
[https://en.wikipedia.org/wiki/Counter-battery_radar](https://en.wikipedia.org/wiki/Counter-battery_radar)
As another comment noted, ballistic trajectories aren’t limited to starting at 45 degrees.
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