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.

[ 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?

Describe motion

Position locates the object, velocity is the rate of change of position, and acceleration is the rate of change of velocity. Distance and speed are scalar; displacement and velocity are directed quantities.

Use the right model

For uniform acceleration:

$v=u+at,\quad s=ut+ rac12at^2,\quad v^2=u^2+2as$

For projectiles without drag, solve horizontal and vertical components with a shared time. Do not use these equations when acceleration is non-uniform.

Check the boundary

Ask whether the quantity is average or instantaneous, whether the route or endpoints matter, whether acceleration is constant, and whether a neglected force such as drag changes the model.

A.1.9—Fluid resistance on projectiles

Explain How Fluid Resistance Changes Projectile Motion

Retrieve the A.1 Kinematics Model

A.1.9 Exam Analysis