A projectile's flight path is determined mainly by its release velocity, release angle, release height, gravity, and aerodynamic forces. In real sporting situations, air resistance, wind, the projectile's shape and surface, and spin also affect its trajectory.
Release velocity has horizontal and vertical components:
A greater horizontal component usually increases horizontal displacement, while a greater vertical component increases flight time and maximum height. After release, gravity accelerates the projectile vertically downward at approximately , producing a curved, approximately parabolic trajectory when aerodynamic forces are ignored.
| Factor | Effect on the flight path |
|---|---|
| Release speed | Greater speed usually increases range and maximum height. |
| Release angle | Changes the balance between horizontal and vertical velocity. A larger angle usually gives more height but less horizontal velocity. |
| Release height | A higher release point increases flight time and can increase range. |
| Gravity | Pulls the projectile downward and continuously changes its vertical velocity. |
| Drag force | Acts opposite to motion relative to the air, reducing speed and range. It depends on air density, speed, frontal area, shape and surface texture. |
| Wind | Changes the projectile's velocity relative to the air, affecting drag and lateral or horizontal displacement. |
| Spin | Produces the Magnus effect, creating a lift force that can make the projectile curve, dip or remain airborne longer. |
For equal release and landing heights with no air resistance, range is:
This simplified model predicts a maximum range at . A common misconception is that is always the optimum release angle. In sport, unequal release and landing heights, drag, spin and technique mean the optimum angle is often different.
For an IB SEHS explain question, identify each factor and state the mechanism by which it changes range, height, flight time or direction. Distinguish the ideal projectile model from real fluid-mechanics effects such as drag and Magnus lift.
