## Parabolic Trajectories

Here are some formulae, related to the kinematic equations (see my post), about parabolic trajectories. These concern, for example, ballistics under gravity, ignoring air resistance.

These formulae assume that the target is at the same height (defined as zero) as the source; that is, the field is a horizontal line or plane through the origin:

launch angle from the horizontal: $\alpha$;
launch speed (scalar; not velocity, which is a vector) : $u$;
acceleration due to gravity $g = 9.80665~m/s^2$;

maximum height attained: $h = u^2 \sin^2 (\alpha) / 2g$;
duration of flight: $t = 2u \sin (\alpha) / g$;
range: $r = u^2 \sin (2 \alpha) / g$;
shape: $h/r = \tan (\alpha) / 4$.