Ballistic trajectories are typically calculated within a coordinate system having a horizontal x-axis and a vertical y-axis, with the initial position at the intersection of the axes. The initial velocity (Vo) is then resolved into its horizontal and vertical components. The horizontal initial velocity (Vox) is the initial velocity multiplied by the cosine of the initial angle (theta). The vertical initial velocity (Voy) is the initial velocity multiplied by the sine of the initial angle (theta).
The distance an object has traveled in the x-direction in feet is calculated by multiplying the initial horizontal velocity (Vox) in feet per second by the time in flight (t) in seconds. The position of the object in the y-direction is calculated by multiplying the initial vertical velocity (Voy) by the time (t) and then subtracting the gravitational effect, which is the time (t) squared multiplied by the gravitational constant (g) and divided by 2.
The distance an object will travel in feet (R) given a set of initial conditions is calculated by multiplying the square of the initial velocity in feet per second (Vo) times the sine of two times the initial angle (theta) and dividing the result by the gravitational constant (g).
The total time of flight in seconds (tf) of a ballistic object is calculated by dividing two times the initial vertical velocity (Voy) by the gravitational constant (g).
The highest point in the ballistic trajectory in feet (hp) is calculated by squaring the initial vertical velocity (Voy) and dividing the result by 2 times the gravitational constant (g).