A.1.9—Fluid resistance on projectiles

Drag opposes instantaneous velocity

Fluid resistance acts opposite the projectile's velocity and usually grows with speed. Its direction changes through the flight, so the resultant acceleration is not the constant downward $g$ of the ideal model.

Quantity	Qualitative effect of fluid resistance
Trajectory	No longer a symmetric parabola; descent is typically steeper
Horizontal velocity	Decreases because drag has a component opposite horizontal motion
Vertical acceleration	On ascent, downward drag makes downward acceleration greater than $g$ ; on descent, upward drag makes it less than $g$
Maximum height and range	Both are reduced for the same launch conditions
Time of flight	Ascent is shortened, while descent can be lengthened by upward drag; the total change is not universally one direction
Terminal speed	During a long fall, increasing drag can balance weight so resultant force and acceleration become zero

Use the force direction

Before the peak, drag has horizontal and downward components; after the peak, it has horizontal and upward components. Therefore acceleration is not determined by velocity alone and changes continuously.

Terminal-speed condition

For vertical descent, terminal speed is reached when upward drag (and any buoyancy included in the model) balances weight. The object then continues at constant downward velocity.

Common trap

Zero acceleration at terminal speed does not mean zero velocity. At the top of a projectile path, vertical velocity may be zero while acceleration remains non-zero.

How it is assessed

The evidence compares actual motion with an ideal no-drag path and asks where acceleration has greatest magnitude during a drag-affected vertical throw.

Command terms

Describe / Identify / Compare

What earns marks

State the direction of drag and connect its changing magnitude to the resultant acceleration. For vertical motion, identify the point where drag is greatest or where drag balances weight; for a projectile, compare speed, range, height and symmetry with the no-resistance model.

Watch for

Assuming acceleration is always g when drag is present, or assuming the trajectory remains a symmetric parabola.

Representative question

[Maximum number: 1]

The diagram shows the path of a ball in the absence of air resistance. Q is the highest point of the ball's trajectory and a is the vertical acceleration at Q . At impact the velocity makes an angle $\theta$ to the horizontal.

Three statements about the actual motion of the ball when there is air resistance are:

I. Q is lower.
II. a remains the same.
III. $\theta$ increases.

Which statements are correct?

I and II only

I and III only

II and III only

I, II and III

A.1.9—Fluid resistance on projectiles

Explain How Fluid Resistance Changes Projectile Motion

A.1.9 Exam Analysis

Assessment in practice

Question 1