Ballistics A.K.A. The Physics

There are three aspects of ballistics: internal, external and terminal. 

•      Internal - is what happens inside the firearm from when a bullet is entered until it leaves the end of the barrel.
•     Terminal - has to do with what happens as soon as the bullet enters the target.
•      External - is what the bullet does while in flight.  This is what we want to take a closer look at.

Once a bullet is launched its trajectory is determined by its velocity, shape and weight.

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Now let’s go through this step by step looking at three parts: time aloft, maximum height and horizontal distance.  This is all done assuming no wind or air resistance.

Time aloft

1. Determine the angle (θ) of the bullets initial arc.
2.  If angle is between bullets initial trajectory and horizontal  then the bullets initial vertical velocity = V_initial X Sin(θ)
3.   Time aloft, t, is found using a position equation:

y((f) = v(i) x sin(θ) t - (0.5) g x t^2 , where g = 9.8 meters / sec^2

Max height

1.       If θ<0 the max height is just the initial height.

2.       Next take the t from time aloft and plug that into a height equation

            y = v(i) x sin(θ) x t - 4.9 t^2

Distance

1.       Calculate the bullets initial horizontal velocity by using v(i) x cos(θ).

2.       Plug in t from when the bullet reaches y(f) into the distance formula.

            x(f) = v(i) x cos(θ) x t

3.