Ballistics with air resistance
Compare the trajectory of a projectile with and without air resistance to understand the effect of drag on range and trajectory shape.
Activity Summary
The student performs shots in the FizziQ Web Ballistics simulation, first without air resistance then with, keeping the same parameters (angle, speed). They compare the superimposed trajectories and observe the asymmetry, the reduced range, and the influence of mass when air resistance is present.
Introduction
In physics classes, we often study projectile motion by neglecting air resistance. But what is the actual effect of air on a projectile? The FizziQ Web Ballistics simulation lets you fire projectiles with identical parameters and compare the trajectories with and without drag. You will discover that air resistance not only reduces the range but also breaks the symmetry of the parabolic trajectory and introduces a mass dependence that does not exist in vacuum.
Learning Objectives
- Observe the asymmetry of the trajectory in the presence of drag
- Understand why mass matters with air resistance but not without
- Find the optimal launch angle with air resistance and compare it to 45°
- Model the drag force as proportional to the square of velocity
Scientific Concepts
Instruments and sensors
Scientific instruments
- FizziQ Web Ballistics simulation
FizziQ Features
- Experiment notebook — used to record the range, angle, and maximum height obtained for each shot, enabling comparison across conditions
Required Materials
- - Computer, tablet, or smartphone with FizziQ Web - Note: the protocol remains adaptable to any comparable simulation tool.
Experimental Protocol
Open the Ballistics simulation in FizziQ Web. Set the initial speed to 25 m/s and the angle to 45°.
Disable air resistance. Launch a shot (REC). Observe the trajectory and note the range in the experiment notebook.
Without changing the parameters, enable air resistance. Launch a new shot. The second trajectory is superimposed on the first for comparison.
Compare the two trajectories: what is the range difference? Is the trajectory with air symmetric like the one without?
With air resistance enabled, perform a series of shots at different angles (30°, 35°, 40°, 45°, 50°). For which angle is the range maximum?
Return to 45° angle. Perform a shot with a low mass, then another with a high mass (if the parameter is available). Compare the ranges.
Disable air resistance and repeat the mass comparison. Does the range change this time?
Record your results in a table: for each condition (with/without air, low/high mass), note the angle, range, and maximum height.
Sketch the trajectories with and without air for the same angle and describe the differences: shape, range, maximum height, symmetry.
Write a conclusion about the effect of air resistance: why is it sometimes a good approximation to neglect it, and when is it not?
Expected Results
Without air, the trajectory is a symmetric parabola and the range at 45° is R = v₀²/g ≈ 63.8 m for v₀ = 25 m/s. With air resistance, the range decreases significantly (30 to 50 m depending on parameters). The trajectory is no longer symmetric: the descending phase is steeper than the ascending phase. The optimal angle drops below 45° (typically 35-40°). Mass matters with air: a heavier projectile travels farther because the drag-to-weight ratio is smaller. Without air, mass has no effect on the trajectory.
Scientific Questions
- How can you explain that the descending phase is steeper than the ascending phase in the presence of air?
- Why does the optimal angle decrease below 45° with air resistance?
- Is the drag force stronger during ascent or during descent? Why?
- In which real-life situations is it justified to neglect air resistance?
- How would the trajectory change if the drag force were proportional to v instead of v²?
Scientific Background
Without air resistance, the projectile's motion depends only on gravity. Mass cancels from the equation (**a = g** regardless of m), so the trajectory is identical for all masses.
The **drag force** exerted by air is proportional to the square of velocity: **F = ½ × ρ × Cx × A × v²**, where ρ is the air density, Cx is the drag coefficient, and A is the cross-sectional area. This force always opposes the velocity.
With air resistance, the projectile's acceleration becomes **a = g - (F/m)**. The term F/m decreases as mass increases, which is why a heavier projectile is less affected by air: it has more inertia relative to the drag force.
The trajectory with air is no longer symmetric because the projectile loses speed throughout the flight. During ascent, drag and gravity both oppose the motion. During descent, drag opposes gravity, so the fall is slower but steeper.
The **optimal angle** drops below 45° because air resistance penalizes high trajectories more heavily (longer path through the air, higher speeds at the apex). Depending on conditions, the optimal angle can be 30-40°.
Extensions
- Compare the ranges with and without air for the same angle and plot the ratio as a function of angle
- Investigate the effect of the drag coefficient by changing it while keeping other parameters fixed
- Compare the trajectories of a tennis ball and a cannonball launched with the same speed and angle
- Find the angle that maximizes range with air resistance for several different speeds
Frequently Asked Questions
How do I enable air resistance in the simulation?
In the simulation settings, enable the "Air resistance" option. Two additional parameters appear for the drag coefficient and cross-sectional area.
Why is the range not exactly v₀²/g at 45° without air?
Check that air resistance is truly disabled and that the launch height is at ground level. Rounding in the simulation may cause slight deviations.
The trajectories with and without air look identical at low speed. Is this normal?
Yes. The drag force is proportional to v², so at low speeds it is very small compared to gravity. The effect becomes significant above about 10-15 m/s for typical projectiles.
Why is the trajectory with air not a parabola?
A parabola requires constant horizontal velocity and constant vertical acceleration (g). Air resistance reduces horizontal velocity and modifies vertical acceleration, breaking both conditions.
Detailed Description
The student performs shots in the FizziQ Web Ballistics simulation, first without air resistance then with, keeping the same parameters (angle, speed). They compare the superimposed trajectories and observe the asymmetry, the reduced range, and the influence of mass when air resistance is present. FizziQ Web runs the simulation directly in the browser and lets the student record range, angle, and height values in the experiment notebook to build a comparison table.
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