Projectile Motion
Projectile motion describes the flight of an object or the human body once it is travelling through the air, no longer in contact with the ground or another surface providing force.
- A ball becomes a projectile the moment it leaves a performer's foot, hand or racket in a kick, throw or hit; the human body itself acts as a projectile in events such as the long jump, high jump or a gymnastics vault, once it leaves the ground
Angle of Release
The angle of release is the angle between the horizontal and the direction the projectile is travelling at the moment it is released, and it is one of three factors (alongside speed and height of release) that determine a projectile's horizontal displacement – the straight-line horizontal distance covered from release to landing.
- When release height and landing height are equal, the optimum angle of release for maximum horizontal distance is 45° (ignoring air resistance) – this applies to a long jumper, who takes off from and lands on the same level ground
- When release height is lower than landing height, the optimum angle needs to be greater than 45° – e.g. shooting a basketball, where the ball is released below the height of the ring
- When release height is higher than landing height, the optimum angle needs to be less than 45° – e.g. the shot put, where the athlete releases from hand height, well above the ground where it lands. In practice, elite shot putters typically use a release angle of around 26-38°, since a lower angle allows greater release speed to be generated, and the ideal angle for any individual also depends on their size, strength and technique
Speed and Height of Release
- A greater speed of release increases horizontal displacement – e.g. in the shot put, the speed generated by the athlete's shift/rotation across the circle determines how fast the shot leaves the hand, and a faster release travels further
- A greater height of release also increases horizontal displacement, since gravity acts on the projectile for a longer overall flight, giving it more time and space to travel horizontally before landing – e.g. a taller cricket fielder releasing a throw from a greater height will, all else being equal, achieve greater horizontal distance than a shorter fielder using the same release angle and speed; a shorter fielder would need to alter either their angle or speed of release to match that distance
Parabolic vs Non-Parabolic Flight Paths
Once in the air, a projectile's flight path is shaped by two opposing forces: its weight (pulling it down due to gravity) and air resistance (opposing its motion through the air).
- A parabola is a smooth, symmetrical curve. Projectiles with a large weight relative to a small air resistance force tend to follow a true parabolic flight path – e.g. a shot put, which is heavy and compact, so weight dominates over the comparatively small air resistance acting on it throughout flight
- Lighter projectiles, or those with an irregular shape that increases drag, are affected more heavily by air resistance and follow a distorted (non-parabolic) flight path instead – e.g. a badminton shuttlecock, which starts a serve at high velocity from the racket but slows rapidly and loses its symmetrical curve as air resistance increasingly dominates over its very light weight
- The longer a projectile remains in flight, the more time air resistance has to act on it and distort its path – meaning slower, longer-duration flights are generally more susceptible to non-parabolic distortion than fast, short ones
Vector Components of Parabolic Flight
Because a projectile released at an angle has both upward and forward motion, its velocity at release can be broken down into two separate vector components, each shown as an arrow whose length represents its size (magnitude):
- The horizontal component represents the sideways/forward motion of the projectile. Where air resistance is negligible (as with a shot put), this component stays constant in size throughout the entire flight, since nothing is acting to speed it up or slow it down horizontally
- The vertical component represents the upward/downward motion of the projectile, and – unlike the horizontal component – is constantly affected by gravity. It starts large and positive at release (moving upward away from the athlete), shrinks to zero at the peak of the flight (the highest point, where the projectile is momentarily moving purely horizontally), and then grows increasingly negative as gravity pulls the projectile back down toward landing
- Combining the horizontal and vertical component vectors at any instant produces a single resultant vector, which represents the projectile's true direction and speed of travel at that point in its flight