Living in a physical world II. The bio-ballistics of small projectiles

Many animals jump; many plants shoot their seeds. While ‘many’ may not imply ‘most’, terrestrial life is rife with examples of ballistic motion, motion in which a projectile gets all of its impetus prior to launch. For most of us, the trajectories of projectiles appeared briefly early in a basic physics course. Some tidy equations emerged in unambiguous fashion from just two facts. A projectile moves horizontally at constant speed; only the downward acceleration of gravity (g) alters its initial vertical speed. Where launch and landing heights are the same, a simple formula links range (d) with launch speed (vo) and projection angle (Θ0) above horizontal: