Air or fluid resistance generally reduces a projectile’s range and eventually limits its downward speed to a constant terminal speed. Unlike the no-resistance model, the trajectory is not perfectly parabolic and is not symmetric.
The Reasoning and Mechanism
Fluid resistance is a force that opposes the projectile’s velocity relative to the fluid. Its magnitude usually increases with speed, so the acceleration is no longer constant; therefore, the standard uniformly accelerated motion equations cannot describe the complete flight directly.
| Stage or quantity | Effect of fluid resistance |
|---|---|
| Horizontal motion | Drag acts opposite the horizontal velocity, so horizontal speed continually decreases. The projectile covers less horizontal distance. |
| Ascent | Drag and weight both have downward components, so the projectile slows more rapidly than without resistance. It reaches a smaller maximum height sooner. |
| Highest point | Vertical velocity is zero momentarily, but horizontal drag remains because horizontal velocity is not zero. Acceleration is therefore not simply zero. |
| Descent | Drag acts upward, opposing downward motion. The projectile approaches terminal speed. |
| Trajectory | The descending path is typically steeper than the ascending path, producing an asymmetric, non-parabolic trajectory. |
For vertical descent, terminal speed occurs when the upward drag force equals the downward weight:
The resultant force is then zero, so by Newton’s second law, acceleration is zero and the projectile continues downward at constant speed. Terminal speed is not reached instantly; it is approached as drag increases with speed. For example, if drag is proportional to speed, the terminal condition is , giving .
A common misconception is that terminal speed means the projectile has stopped. It has not: its velocity is constant because the forces are balanced.
Exam Technique
This is SL and HL content in A.1 Kinematics. For an Explain question, link drag’s direction to changes in velocity, acceleration, range, time of flight and trajectory. State that the constant-acceleration projectile equations apply only when fluid resistance is neglected; avoid claiming that drag always has a fixed magnitude.