Fluid mechanics
· Projectile motion through air is determined by factors and forces acting on the object during flight.
· A projectile’s flight path is primarily determined by its initial velocity and angle of projection.
· Higher initial velocity generally allows the object to travel further, depending on the angle and resistance.
· Angle of projection affects the shape and range of the trajectory; in sport, the “best” angle depends on the task.
· Height of release relative to the target affects the desired flight path, e.g. throwing to a higher, lower or same-level target.
· The object’s flight path is influenced by its weight relative to air resistance.
· Heavier objects are generally less affected by air resistance than lighter objects of similar shape and size.
· In exam answers, link projectile motion to sporting examples such as javelin, basketball shots, long jump take-off, football passes or tennis lobs.
This image helps students visualize how a projectile follows a curved trajectory after release. It is useful for linking initial velocity, angle of projection and flight path in sport. Use it when revising projectile examples such as throws, kicks and jumps. Source
Key projectile factors in sport
· Initial velocity = speed and direction of the object at release; it strongly affects distance, height and time in flight.
· Angle of projection = angle at which the object is released; it affects the balance between vertical height and horizontal distance.
· Height of release = vertical position of the object at release compared with the target or landing point.
· If the target is lower than the release point, a lower projection angle may be effective.
· If the target is higher than the release point, a higher projection angle may be required.
· Air resistance opposes motion and can reduce range, alter trajectory and affect accuracy.
· The effect of air resistance depends on the object’s weight, shape, surface area and speed through the air.
HL only: environmental conditions and external forces
· Environmental conditions affect the external forces acting on an object moving through air or water.
· Key environmental conditions include temperature, humidity, air pressure, wind, salinity of water and altitude.
· Wind can increase or decrease range depending on whether it acts with or against the projectile.
· Altitude and air pressure can change the resistance experienced by a moving object.
· Water salinity can affect buoyancy because it changes the density of the fluid.
· In exams, explain how environmental changes may affect performance, fairness, equipment choices or strategy.
HL only: buoyancy, lift and drag
· Buoyancy, lift and drag act on a body moving through a fluid, meaning air or water.
· These forces have a measurable effect on the object’s or body’s path.
· Buoyancy depends on the density of the fluid and the volume of fluid displaced.
· In water-based sports, buoyancy affects body position, flotation and efficiency of movement.
· Lift can affect the path of objects or bodies moving through fluids, especially where there is a pressure difference.
· Drag is a resistive force that opposes motion through a fluid.
· Types of drag: surface drag, form drag and wave drag.
· Drag can be altered by manipulating the environment or the moving object.
· Examples include changes to body position, equipment design, clothing, surface texture or technique.
This diagram shows how an object in a fluid experiences an upward buoyant force related to displaced fluid. It supports the IB point that buoyancy depends on fluid density and volume displaced. It is especially useful for swimming, rowing and water-based sport examples. Source
This image helps explain how changing angle of attack alters lift as a body or object moves through a fluid. In sport, this can be linked to balls, equipment or body positions that redirect airflow or water flow. It is useful for HL explanations involving lift and performance effects. Source
HL only: Bernoulli’s principle, angle of attack and Magnus effect
· A projectile travelling through a fluid may be affected by Bernoulli’s principle, angle of attack and the Magnus effect.
· Bernoulli’s principle links fluid speed and pressure differences, which can contribute to lift.
· Angle of attack = angle between the object/body and the direction of fluid flow; it can change lift and drag.
· Magnus effect occurs when a spinning object moving through a fluid experiences a force that curves its path.
· Sporting examples include topspin, backspin, swing, swerve and curl in balls.
· To score highly, connect these ideas to how athletes manipulate spin, surface, speed, angle and technique.
This source supports understanding of how airflow and pressure differences relate to lift. It is useful for HL explanations of Bernoulli’s principle without overcomplicating the physics. Link it to sport examples where airflow changes the path of a ball or object. Source
HL only: sporting, ethical and regulatory implications
· Fluid mechanics can create sporting advantages through equipment, clothing, technique or environmental manipulation.
· Reducing drag can improve speed in sports such as swimming, cycling, skiing, bobsleigh and speed skating.
· Increasing or controlling lift can improve projectile or object movement in sports involving balls, discs or aerodynamic equipment.
· Equipment changes may raise ethical issues if they create an unfair advantage.
· Regulatory bodies may restrict equipment if it changes performance too much or threatens fairness.
· Strong exam answers should consider both performance benefits and fairness/regulation.
Checklist: can you do this?
· Explain how initial velocity, angle of projection and height of release affect a projectile’s flight path.
· Apply projectile motion ideas to sporting examples such as throwing, kicking, jumping or striking.
· Describe how air resistance affects flight path depending on the object’s weight and resistance encountered.
· HL: explain how buoyancy, lift and drag affect movement through air or water.
· HL: discuss ethical and regulatory implications of using fluid mechanics to improve performance.