This laboratory explores the principles of projectile motion and investigates the role of air resistance in real-world conditions. Projectile motion describes the movement of an object launched into the air under the influence of gravity. In an idealized model, the only force acting on the object after launch is gravity, resulting in a predictable parabolic trajectory. However, in practical situations, additional forces such as air resistance can influence the motion and lead to deviations from theoretical predictions.
In this experiment, a marble is launched from a ramp equipped with a springboard inclined at 31°, and its motion is observed as it travels through the air and lands in a sandbox. By varying the starting position of the marble along the ramp, students modify the initial conditions of the motion, particularly the exit speed. These variations allow for the investigation of how physical parameters such as time of flight, horizontal distance, and exit velocity influence the trajectory.
The laboratory emphasizes the comparison between theoretical calculations and experimental measurements. Students will apply kinematic equations to predict the motion of the marble in the absence of air resistance and then compare these predictions with observed data. This comparison provides insight into the limitations of ideal models and highlights the impact of real-world forces such as air resistance.
Through this activity, students develop a deeper understanding of motion in two dimensions, the independence of horizontal and vertical components of motion, and the importance of experimental validation in physics. The lab also reinforces the use of precise measurement techniques and critical analysis when interpreting results.
Educational Goals
Understanding projectile motion
Develop a clear understanding of projectile motion as a two-dimensional phenomenon involving independent horizontal and vertical components. Learn how gravity affects vertical motion while horizontal motion remains uniform in the absence of air resistance.
Application of kinematic equations
Apply kinematic equations to calculate key physical parameters such as time of flight, horizontal displacement, and velocity components. Use these equations to model the motion of the marble under ideal conditions.
Analysis of initial conditions
Examine how changes in the starting position on the ramp affect the exit speed of the marble and, consequently, its trajectory. Understand the relationship between initial velocity and the resulting motion.
Experimental measurement and data collection
Use sensors to measure time of flight, horizontal distance, and exit speed accurately. Develop skills in recording and organizing experimental data in a clear and structured manner.
Comparison between theory and experiment
Compare theoretical predictions with experimental results and evaluate the degree of agreement. Calculate relative differences and assess whether the discrepancies are significant.
Understanding the role of air resistance
Determine whether air resistance has a measurable effect on the marble’s motion. Analyze deviations from ideal projectile motion and interpret them in terms of real-world forces.
Protocol
Introduction
- The setup in front of you reproduces a ramp equipped with a springboard inclined at 31° and a sandbox for the landing of a ball.
- With the practical laboratory, you must determine whether air resistance influences the ball’s trajectory once it has left the springboard.
- To do this, you will collect certain physical parameters of the ball’s motion during its flight that are likely to be affected by the choice of the place on the ramp where the descent begins.
Procedures
- Position one of the stopwatch sensors on the board at the end of the ramp, and the other sensor at the end of the sandbox.
- Position the ball on the ramp at the highest point.
- Press the “Start” button to release the ball.
- Observe the demonstration.
- The data from the demonstration are entered in the results table.
- Repeat steps 2 to 5 by successively positioning the ball at the three other lower positions.
Questions
- Once the data has been collected, you will need to answer the following questions:
a) What are the collected parameters?
b) How to calculate the time of flight and the distance in the sandbox if no resistance was offered by the air?
Consider that the upward slope has an inclination of 45° and a height of 0.12 m.
c) Compare the data obtained in the laboratory to the theoretical data (calculated in the previous step).
d) For each trial (height on the ramp), determine whether air resistance is negligible or not.
Anticipated Outcomes
As the starting point on the ramp is lowered, the marble’s initial speed upon leaving the ramp is expected to decrease. This change in speed will directly affect measurable parameters such as horizontal range, flight time, and maximum height. If air resistance is negligible, the trajectories should closely match theoretical predictions for projectile motion, and differences in motion should be fully explained by variations in initial velocity alone. The path of the marble should remain parabolic, and the horizontal and vertical components of motion should remain independent. If air resistance is significant, deviations from ideal motion may appear, such as reduced range, asymmetrical trajectories, or non-linear changes in flight parameters as initial speed increases.
Theoretical data (actual data may vary)
| Starting point | Time of flight (Δt) | Horizontal distance (Δx) | Exit speed (vexi) |
| 0.47m | 0.31 s | 0.74 m | 2.21 m/s |
| 0.37m | 0.28 s | 0.67 m | 1.87 m/s |
| 0.28m | 0.23 s | 0.60 m | 1.50 m/s |
| 0.19m | 0.20 s | 0.38 m | 0.99 m/s |
a) What are the collected parameters?
Baseline variables
- The inclination of the descending ramp θd_ramp is 31° and the height hd_ramp is variable (0.47, 0.37, 0.28, 0.19 m)
- The inclination of the ascending ramp θa_ramp is 45° and the height ha_ramp is 0.12m.
- The acceleration due to gravity a is 9.8 m/s2
- The final height hfinal is 0 m.
We gather also the time of flight Δt, the horizontal distance Δx, as well as exit speed vexit, to compare theory to data.
Considering baseline variables and experimental data, we can calculate the initial, vertical and horizontal speed of the marble:
Exit vertical speed of the marble, vy_exit in m/s
vy_exit = vexit* sin θa_ramp
Exit horizontal speed of the marble, vx_exit in m/s
vx_exit = vexit* cos θa_ramp
b) How to calculate the flight time and the distance in the sandbox if no resistance were offered by the air?
Marble theoretical time of flight (Δt)
We’ll use the second kinematic equation
hfinal = ha_ramp+ vy_exit * Δt + 0.5*a*Δt2
Marble theoretical horizontal distance (Δx)
The horizontal distance, Δx, is calculated using
Δx =vx_exit * Δt
c) Compare the data obtained in the lab to the theoretical data (calculated in the previous step)
You’ll obtain the marble theoretical time of flight (Δt) and the marble theoretical horizontal distance (Δx). You can then compare these experimental values to these theoretical values with
experimental Δt / theoretical Δt *100 and
experimental Δx / theoretical Δx *100
d) For each trial (height on the ramp); determine whether air resistance is negligible or not
Results should demonstrate that air resistance is between 10 and 20%, which is not negligible.
In summary
- Take note of the baseline variables.
- Measure the physical parameters of the marble’s motion: time of flight Δt, the horizontal distance Δx, as well as exit speed vexit,.
- Calculate the initial, vertical and horizontal speed of the marble.
- Calculate the flight time and the distance in the sandbox if no resistance were offered by the air.
- Compare the data obtained in the lab to the theoretical data.
- Compare these experimental values to these theoretical values with experimental Δt / theoretical Δt *100 and experimental Δx / theoretical Δx *100.
Overall, the experimental approach used in this investigation is appropriate for determining whether air resistance affects the trajectory of the marble. The method allows for a comparison between theoretical predictions and measured values, which is essential for evaluating the validity of the projectile motion model. However, several sources of uncertainty may have influenced the precision of the results.
One major source of uncertainty arises from the measurement of the time of flight. When timing is done manually, it is difficult to synchronize the exact moment the marble leaves the ramp and the moment it impacts the ground. This human reaction time introduces a significant margin of error. Using video analysis or frame-by-frame recording would improve timing accuracy.
Another important source of uncertainty is related to the observation of the marble’s impact point. Whether the landing position is observed directly or determined from video footage, it is challenging to identify the exact point of contact with the ground. This uncertainty often exceeds the intrinsic precision of the measuring instrument used to determine the horizontal distance.
Finally, when the initial speed is measured using a photodiode system, uncertainties may arise from the very short time interval during which the marble passes through the light beam. Small misalignments between the beam and the marble’s diameter can lead to an overestimation of the initial speed and, consequently, of the theoretical range.
To improve the precision of the results, the experiment could be refined by using clearer reference markers at the landing point, and more controlled alignment of measurement devices. These improvements would reduce uncertainty and strengthen the reliability of the conclusions.
Summary of Assignment by Grade Range
Grade 9–10 (Introductory Level)
At the introductory level, this laboratory provides students with a first structured experience of projectile motion and the idea that motion in physics can be both observed and explained using simple relationships. The emphasis is placed on qualitative understanding, observation, and safe laboratory practices rather than complex calculations.
Students explore how a marble behaves once it leaves the ramp and travels through the air. They observe that changing the starting position on the ramp affects how far the marble travels and how long it remains in the air. These observations help students recognize that the initial conditions of motion, particularly speed, play a key role in determining the trajectory.
At this stage, students are introduced to the idea that motion can be separated into horizontal and vertical components, even if they do not yet perform detailed calculations. They begin to understand that gravity acts vertically while horizontal motion continues independently. The concept of air resistance may be introduced qualitatively, allowing students to notice that real motion may differ slightly from ideal predictions.
Teacher guidance is essential. Instructions are broken down step by step, and students are supported in recording observations clearly and accurately. The focus is on developing confidence in the laboratory environment, learning how to follow procedures, and making basic comparisons between different trials.
Learning outcomes at this level include:
- Describing projectile motion using observations
- Recognizing that initial speed affects distance and time of flight
- Identifying horizontal and vertical components of motion conceptually
- Following laboratory procedures safely and accurately
- Recording and comparing observations in a structured way
Grade 11 (Intermediate Level)
At the intermediate level, the laboratory shifts toward a more quantitative and analytical approach. Students are expected to apply kinematic equations to calculate theoretical values for time of flight and horizontal distance, assuming no air resistance. The separation of motion into horizontal and vertical components becomes explicit and is used to solve problems.
Students calculate velocity components using trigonometric relationships and apply equations such as:
vy_exit = vexit* sin θa_ramp and vx_exit = vexit* cos θa_ramp
as well as time-dependent equations for vertical motion. They then use these results to determine theoretical flight time and horizontal range.
A key component at this level is the comparison between theoretical and experimental results. Students calculate percentage differences between measured and predicted values and analyze whether these differences are significant. This process introduces them to the concept of model limitations and the role of simplifying assumptions in physics.
Students are also expected to consider real-world effects, particularly air resistance. They analyze whether air resistance is negligible or not by examining the magnitude of discrepancies. Additionally, they begin to recognize sources of experimental uncertainty, such as timing accuracy, measurement precision, and sensor alignment.
Learning outcomes at this level include:
- Applying kinematic equations to predict projectile motion
- Calculating velocity components and flight parameters
- Comparing experimental data with theoretical predictions
- Evaluating the effect of air resistance on motion
- Identifying and explaining sources of experimental error
- Demonstrating increasing independence in laboratory work
Grade 12 / College Level (Advanced Level)
At the advanced or pre-university level, the laboratory becomes an exercise in model validation, critical thinking, and scientific reasoning. Students are expected not only to perform calculations accurately but also to understand the assumptions and limitations of the projectile motion model.
Students analyze the equations used in greater depth and understand why horizontal and vertical motions are treated independently in ideal conditions. They evaluate how air resistance introduces a coupling between these components and leads to deviations from parabolic motion. The concept of non-negligible forces is explored more rigorously.
A detailed error analysis is expected. Students distinguish between systematic errors (such as calibration issues or consistent measurement bias) and random errors (such as variations in release timing or environmental conditions). They assess how these uncertainties propagate through calculations and influence final results.
Students are also expected to justify their conclusions using both quantitative data and theoretical reasoning. For example, they must determine whether a 10–20% difference between theoretical and experimental values is significant and explain what this implies about the role of air resistance.
Communication skills are emphasized at this level. Students must present their results clearly, structure their reasoning logically, and use appropriate scientific terminology. The laboratory becomes a preparation for post-secondary studies, where precision, clarity, and critical evaluation are essential.
Learning outcomes at this level include:
- Evaluating the validity of physical models and assumptions
- Performing detailed quantitative and error analysis
- Interpreting the role of air resistance in projectile motion
- Justifying conclusions using evidence and reasoning
- Communicating scientific findings in a structured and professional manner
Laboratory essentials
Instruments
- Ramp with 31° incline
- Projectile marble
- Sandbox
- Photodiodes & timer
- Camera