![]() In case of $y$-axis we have to consider the direction as well as the magnitude of the vectors, A projectile passes through the same height twice (except maximum height). Therefore a $g$ can appear.īut I would try to find the actual trajectory length by first making a trajectory equation ( see here for example go down to the "Parabolic Trajectory" headline) and then to use the length formula on it ( see here). I am not sure this is a correct formula for the trajectory length (the length of the flight path).įirstly, remember that here on Earth, while there is no horizontal acceleration $a_x=0$, there is a vertical acceleration, which has a known value: $a_y=g$ (pointing downwards, so remember a proper sign). If we consider the equation $S=u_xt+\frac 12gt^2$, then it gives the displacement or the total path of the trajectory? You might have to calculate this time first. If you need the total horizontal distance travelled, then do the same, but plug in the total time as $t$ instead (the time when the object lands again).
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