High School Rocket Physics Lab

Learning Objectives

By the end of this lesson, students will be able to:

Kinematics

Derive muzzle velocity from measured range and launch angle using projectile motion equations; calculate maximum height and time of flight.

Energy Analysis

Calculate work done by compressed air on the rocket and compare to kinetic energy at launch; analyze energy losses to drag.

Data Modeling

Fit regression models to experimental data, evaluate goodness of fit, and use models to make predictions.

Computational Modeling

Use computer simulation to predict rocket performance, then validate predictions against experimental results.

Materials Needed

Compressed air rocket launcher with pressure gauge (PSI)
Foam rockets with known masses
Digital scale (0.1g precision)
High-speed camera or slow-motion phone app (optional)
Safety glasses for each student
Tape measures (100+ ft / 30+ m)
Stopwatches (0.01s precision)
Laptops/tablets with internet access
Scientific calculators
Graphing software (Desmos, Excel, or graphing calculators)
Lab notebooks or data sheets

Key Equations

Projectile Motion (Ideal, No Air Resistance)

x = v₀ cos(θ) · t

y = v₀ sin(θ) · t - ½gt²

R = (v₀² sin(2θ)) / g

h_max = (v₀² sin²(θ)) / 2g

Where: v₀ = muzzle velocity, θ = launch angle, g = 9.8 m/s², R = range, h = max height

Energy & Work

KE = ½mv²

W = F · d

v = √(2E/m)

Aerodynamic Drag

F_D = ½ C_d ρ A v²

Where: C_d = drag coefficient, ρ = air density (~1.2 kg/m³), A = cross-sectional area, v = velocity

Vocabulary

Muzzle Velocity

The speed of a projectile as it leaves the launcher

Projectile Motion

Motion under gravity after initial launch

Kinetic Energy

Energy of motion: KE = ½mv²

Work

Energy transferred by a force: W = F·d

Drag Coefficient

A dimensionless number representing air resistance based on shape

Regression

Finding a mathematical function that best fits data

R² (R-squared)

A measure of how well a model fits the data (0 to 1)

Adiabatic Expansion

Gas expansion without heat transfer (applies to rapid air release)

Lesson Procedure

1 15 minutes

Theoretical Framework

Review projectile motion equations and set up the analysis framework.

Review the kinematic equations for projectile motion
Derive the range equation: R = (v₀² sin(2θ)) / g
Discuss: "Why is 45° optimal for maximum range?" (sin(2·45°) = sin(90°) = 1)
Introduce the key question: "Can we determine the muzzle velocity from the measured range?"
Rearrange the range equation to solve for v₀:

Deriving Muzzle Velocity from Range

R = (v₀² sin(2θ)) / g

v₀² = Rg / sin(2θ)

v₀ = √(Rg / sin(2θ))

At 45°: v₀ = √(Rg) since sin(90°) = 1

Have students predict: "If a rocket travels 25 meters at 45°, what's its muzzle velocity?" (Answer: v₀ = √(25 × 9.8) ≈ 15.7 m/s)

2 10 minutes

Computer Simulation Introduction

Introduce the trajectory simulation tool.

Trajectory Calculator

Before launching physical rockets, use the online trajectory calculator to:

Predict expected range for given pressure settings
Explore how mass, angle, and pressure affect trajectory
See the effects of drag coefficient on range
Understand the physics equations in action

Students will later compare simulation predictions to actual results.

Have students input different values and observe changes
Record predictions for the launcher settings you'll use
Discuss: "Why might real results differ from ideal predictions?" (Air resistance, wind, imperfect launches)

3 30 minutes

Data Collection

Systematically collect data to calculate muzzle velocity and analyze energy.

Measure and record: Rocket mass (kg), launch angle (degrees), horizontal range (m), time of flight (s)
Fixed conditions: Same pressure (record PSI), same launcher
Test angles: 30°, 45°, 60° (5 trials each)
For each trial, record: distance, time aloft, observations

Sample Data Collection Sheet

Angle (°)	Trial	Range (m)	Time (s)	Calc v₀ (m/s)	Calc h_max (m)
45	1	24.5	2.21	15.5	6.1
45	2	25.2	2.28	15.7	6.3
45	3	23.8	2.15	15.3	6.0
30	1	22.1	1.56	15.6	3.1
60	1	21.8	2.70	15.5	9.2

Note: If v₀ is consistent across angles, our measurements are reliable!

The "time of flight" method provides an independent check: t = 2v₀sin(θ)/g, so v₀ = gt/(2sinθ). Compare to the range method!

4 20 minutes

Calculations & Analysis

Perform quantitative analysis of the collected data.

Part A: Muzzle Velocity Calculation

For each trial, calculate v₀ using: v₀ = √(Rg / sin(2θ))
Calculate mean v₀ across all trials
Calculate standard deviation to assess consistency
Compare: Do different angles give similar v₀ values? (They should!)

Part B: Maximum Height

Calculate theoretical h_max = (v₀² sin²θ) / 2g for each angle
Compare 30° vs 45° vs 60° - which goes highest?
Verify with time data: h_max at apex when v_y = 0, so t_up = t_total/2

Part C: Energy Analysis

Energy Audit

Given: m = 0.060 kg, v₀ = 15.5 m/s

KE = ½mv² = ½(0.060)(15.5)² = 7.2 J

This is the minimum energy the compressed air transferred to the rocket.

Questions: Where did this energy come from? (Work done by expanding gas) Where does it go during flight? (Gravitational PE at apex, then back to KE, minus drag losses)

5 15 minutes

Regression Analysis

Model the relationship between angle and range.

Plot angle (x) vs. range (y) as a scatter plot
The theoretical model is: R = (v₀²/g) sin(2θ), which is a sinusoidal function
For the limited range of 30°-60°, try fitting a quadratic: R = a(θ-45)² + b
Calculate R² to assess model fit
Use the model to predict: At what angle is range maximized? (Should be near 45°)

If students have access to graphing calculators, use the built-in regression functions. In Desmos, they can fit custom equations to data points.

6 10 minutes

Simulation vs. Reality

Compare experimental results to computer predictions.

Return to the trajectory calculator with measured v₀
Input actual conditions: mass, velocity, angle
Compare predicted range to measured range
Discuss discrepancies: "Why might our rockets travel less far than the ideal prediction?"
Identify sources of error: air resistance, wind, measurement uncertainty, imperfect launch angle

Effect of Drag

Real rockets experience drag: F_D = ½C_dρAv²

This reduces range compared to ideal projectile motion. The simulator can model this if drag coefficient is included.

Key insight: Drag force is proportional to v², so it has the biggest effect right after launch when velocity is highest.

7 10 minutes

Discussion & Conclusions

Synthesize findings and connect to broader physics.

Review key findings: What was the average muzzle velocity? How consistent were the measurements?
Discuss the energy flow: chemical potential (compressed air) → kinetic → gravitational potential → kinetic → thermal (drag losses)
Connect to real applications: How do aerospace engineers use these same principles?
Discuss limitations: What assumptions did we make? (No wind, instant acceleration, point mass)
Propose improvements: How could we get more accurate results?

Assessment Strategies

Lab Report (Formal Write-Up)

Introduction (10%): Background physics, purpose, hypothesis
Methods (15%): Detailed procedure, variables, controls
Data (20%): Complete tables, all calculations shown
Analysis (25%): Graphs, regression, error analysis
Conclusions (20%): Results summary, physics explanation, limitations
Simulation Comparison (10%): Predicted vs. actual, explanations

Calculation Competency

Correctly derive v₀ from range and angle
Calculate kinetic energy at launch
Determine maximum height from initial conditions
Use regression to model data
Propagate uncertainty through calculations

Conceptual Understanding

Students should be able to explain:

Why 45° maximizes range (for ideal projectiles)
Why complementary angles give equal range
How drag affects the trajectory
The energy transformations during flight
Why models differ from reality

Extensions

Advanced: Drag Coefficient Estimation

Compare actual range to ideal range. The difference is due to drag. Using the drag equation and measured deceleration, estimate C_d for the rocket. Typical values: sphere ~0.47, streamlined body ~0.04, blunt cylinder ~0.82.

Advanced: Momentum Analysis

Calculate initial momentum p = mv₀. Estimate the impulse delivered by the launcher (force × time). Use video analysis to estimate the launch time (~0.1s) and calculate the average force.

Advanced: Thermodynamics

For the very ambitious: Model the adiabatic expansion of compressed air. P_exit = P₀(V₁/V₂)^γ where γ = 1.4 for air. Connect this to the energy delivered to the rocket.

AP Physics Application

Frame as an AP Physics C problem: A rocket of mass m is launched with muzzle velocity v₀ at angle θ. (a) Derive the range equation. (b) At what angle is range maximized? (c) If drag force F_D = bv² acts during flight, set up (but don't solve) the differential equation for x(t).

Standards Addressed

Georgia Science Standards (GSE) - Physical Science & Physics

Code	Standard	How This Lesson Addresses It
SPS8	Obtain, evaluate, and communicate information to explain the relationships among force, mass, and motion.	Comprehensive analysis of rocket motion using Newton's Laws and kinematics.
SPS8.a	Plan and carry out an investigation to analyze the motion of an object using mathematical and graphical models.	Systematic data collection, graphing, and regression modeling.
SPS8.b	Construct an explanation based on experimental evidence to support claims in Newton's three laws of motion.	Full lab report with quantitative evidence supporting Newton's Laws.
SPS8.d	Use mathematics to identify relationships between work, mechanical advantage, and simple machines.	Energy analysis: work done by air, kinetic energy of rocket.

NGSS - High School Physics & Engineering

Code	Standard	How This Lesson Addresses It
HS-PS2-1	Analyze data to support the claim that Newton's second law describes the mathematical relationship among net force, mass, and acceleration.	Calculate acceleration from kinematic data; relate to F=ma.
HS-PS2-2	Use mathematical representations to support the claim that momentum is conserved.	Extension: Momentum analysis of launch phase.
HS-ETS1-2	Design a solution to a complex problem based on scientific knowledge, prioritized criteria, and tradeoff considerations.	Optimize rocket design based on physics understanding.
HS-ETS1-4	Use a computer simulation to model the impact of proposed solutions.	Use trajectory calculator to predict and compare to actual results.

Common Core Math - Functions & Statistics

Code	Standard	How This Lesson Addresses It
HSF-IF.B.4	Interpret key features of graphs (intercepts, max/min, increasing/decreasing) in terms of context.	Analyze angle vs. range graph: identify maximum, symmetry.
HSF-IF.B.6	Calculate and interpret average rate of change over a specified interval.	Calculate average velocity during flight phases.
HSF-LE.A.2	Construct linear and exponential functions from a graph, description, or input-output pairs.	Fit models to experimental data.
HSF-TF.A.3	Use special triangles to determine values of sine, cosine, and tangent for π/6, π/4, and π/3.	Calculate sin(2θ) for 30°, 45°, 60° in range formula.
HSS-ID.B.6	Represent data on scatter plots and describe relationships.	Create scatter plots of angle vs. range; identify pattern.
HSS-ID.C.8	Use regression models to analyze bivariate data and make predictions.	Fit quadratic or sinusoidal model to angle vs. range data.

Mathematical Practices

Practice	How This Lesson Addresses It
MP.2 Reason abstractly	Use symbolic equations to represent physical quantities; interpret results in context.
MP.4 Model with mathematics	Apply projectile motion equations to real-world rocket launches.
MP.5 Use appropriate tools	Use calculators, graphing software, and simulation tools strategically.
MP.6 Attend to precision	Use appropriate significant figures; propagate uncertainty.