Projectile motion refers to the motion of an object or human body that is launched into the air and is influenced only by the forces of gravity and air resistance.
Once a projectile is released, it no longer has any self-propulsion, meaning its flight path is entirely predetermined at the precise moment of take-off. In sport, projectiles can be objects, such as a kicked football, a thrown javelin, or a smashed shuttlecock, or they can be the human body itself, such as a long jumper or a diver mid-flight. Understanding the principles governing this motion allows athletes to manipulate their technique to maximise distance, height, or accuracy.
The flight path of a projectile is called its trajectory, and it is typically shaped like a parabola—a symmetrical curve. This trajectory results from two independent components acting simultaneously: a horizontal component and a vertical component.
The horizontal component determines the distance the projectile travels. If air resistance is ignored, horizontal velocity remains constant throughout the flight because no horizontal force is acting to speed it up or slow it down.
The vertical component determines the projectile's height and is continually altered by gravity, which accelerates the projectile downward at a constant rate of $9.81\text{ m/s}^2$. This causes the vertical velocity to decrease on the way up, briefly hit zero at the peak of the flight, and increase on the way down.
The specific shape of a projectile's trajectory and the distance it travels are determined by three main flight factors at the point of release: the angle of release, the velocity of release, and the height of release. The velocity of release is the most critical factor because the initial speed directly determines the magnitudes of both the horizontal and vertical components; the faster an object is thrown or kicked, the farther or higher it will travel.
The angle of release determines the shape of the trajectory. If the release height and landing height are equal, such as kicking a football from the ground to another player on the ground, the optimal angle for maximum horizontal distance is exactly $45^\circ$.
However, in most sporting events, the release height is higher than the landing height because an athlete throws an object from shoulder level or jumps from an elevated position. When the release height is greater than the landing height, the optimal angle of release decreases to less than $45^\circ$—typically around $35^\circ$ to $40^\circ$ for a shotputter or javelin thrower, to maximise horizontal distance. Conversely, if the release height is lower than the landing height, the optimal angle must be greater than $45^\circ$.Finally, air resistance can distort the perfect parabolic shape of a trajectory, turning it into an asymmetrical curve.
The amount of air resistance a projectile experiences depends on its velocity, surface characteristics, and cross-sectional area. A heavy, streamlined object like a shotput is barely affected by air resistance, allowing it to follow a nearly perfect parabola. However, a lightweight object with a large surface area, such as a badminton shuttlecock, experiences significant air resistance. This drag force rapidly reduces its horizontal velocity mid-flight, causing its trajectory to drop steeply at the end rather than following a symmetrical curve.
