Trajectory
A trajectory or flight path is the path that a moving object follows through space as a function of time.
The trajectory has horizontal (x) and vertical (y) position components. If a projectile is launched with an initial velocity v0, at an angle θ from the horizontal plane, then its vertical position can be found from its horizontal position using the following formula. The units of horizontal and vertical position are meters (m).
\[y = xtan\theta -\frac{gx^{2}}{2v_{0}cos^{2}\theta } \]
y = vertical position (m)
x = horizontal position (m)
v0 = initial velocity (combined components, m/s)
g = acceleration due to gravity (9.80 m/s2)
θ = angle of the initial velocity from the horizontal plane (radians or degrees)
we use \[\theta = a \] in our calculation.
