## Vectors and Projectiles Notebook Labs

The following items should be in the Vectors and Projectiles portion of your notebook. They should be clearly organized and easy to find. Use an organizational system and label all work. Each lab will be graded separately.

### VP1. Map Lab

Question:
How do the N-S, E-W legs of a trip compare to the overall displacement of that trip?

Purpose:
To identify the mathematical relationship between the N-S and E-W legs of a trip to the overall displacement for that trip.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section should include the provided table with the required trips and one self-designed trip. The Conclusion/Discussion should identify the mathematical relationship between the legs of the trip and the overall displacement for that trip; the relationship should be general enough to be applied to any trip in order to determine the overall displacement from a statement of the legs. Two of the four trips (at least one of which is a three-legged trip) should be mathematically analyzed to provide the supporting evidence for your conclusion; work should be shown, labeled and discussed in an organized fashion.

### VP2. As the Crow Flies Lab

Question:
What is the as-the-crow-flies displacement from the Physics room (Room 332) to an assigned location in the school?

Purpose:
To determine the as-the-crow-flies displacement from the Physics room (Room 332) to a designated location within the school.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion. The Data section should include a table of the magnitude and the direction of each of your hallway displacements used to reach your assigned destination. The number (or letter) of the destination should be indicated. This section should also include a trigonometric analysis of the data and a scaled vector diagram analysis; the analyses should be organized, labeled and follow-able. All work should be shown for your trigonometric analysis. In the scaled vector diagram: indicate a scale, label the magnitudes of all vectors, place arrowheads on all vectors, draw and label the resultant, identify the measured and scaled-up magnitude of the resultant and identify the direction of the resultant. The Conclusion should respond to the question raised in the Purpose.

### VP3. Where Am I? Lab

Question:
What is the ultimate destination which results from the combination of three displacement vectors?

Purpose:
To identify the ultimate destination which results from the combination of three displacement vectors.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion. The Data section should include the provided table. For each vector, the vector should be sketched and labeled with magnitude and angle with respect to a nearby axis; the N-S and E-W components should be calculated; work should be organized and labeled. The final destination should be identified. The Conclusion responds to the question raised in the Purpose (as always).

### VP4. Road Trip Lab

Question:
What overall displacement (magnitude and direction) and final destination results from the addition of three displacement vectors?

Purpose:
To determine the overall displacement and the final destination which results from the addition of three displacement vectors (beginning in Chicago).

A complete lab write-up includes a Title, a Purpose, a Data section, a Conclusion, and a Post-Lab Questions section. The Data section should include the provided table of displacements; the table should be completed and the resulting displacement should be determined using trigonometry; all work should be clearly shown. The Conclusion (as always) should answer the question posed in the Purpose. The three provided questions should be answered.

### VP5. Crossing the River Lab

Question:
For a boat heading straight across a river, how does an change in the boat speed effect the resulting velocity, the crossing time and the downstream distance? How does a change in current speed effect the resulting velocity, the crossing time and the downstream distance?

Purpose:
To determine the effect of varying boat speeds on the resulting velocity, the crossing time and the downstream distance for a boat which heads straight across a river AND to determine the effect of varying current speeds on the resulting velocity, the crossing time and the downstream distance for a boat which heads straight across a river.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section should include suitable data for investigating the purpose; the data should be organized in tables with column headings and units. The organization of data should reflect your ability to systematically conduct an investigation. The Conclusion/Discussion should respond to the multi-part Purpose of the lab; each conclusion should reference appropriate data in order to provide supporting evidence.

### VP6. Basketball Analysis Lab

Question:
How can the changes (or lack of changes) in the motion quantities (position, velocity and acceleration) of a projectile be described over the course of time?

Purpose:
To describe how the motion quantities (position, velocity and acceleration) of a projectile change (or don't change) over the course of time.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section includes plots of the dx and dy values with respect to time, plots of the vx and vy values with respect to time and plots of the ax and ay values with respect to time. All plots should be clearly labeled. Slope values for the two velocity graphs should be shown and labeled beside each graph. The Conclusion/Discussion should use words to thoroughly respond to the question raised in the Purpose. For each conclusion statement, at least one piece of supporting evidence should be provided; six sentences would be the minimum amount of writing.

### VP7. Projectile Simulation Lab

Question:
How can a vector diagram be used to describe the changes (or lack of changes) in the horizontal and vertical components of velocity and how can such changes (or lack of changes) be described in words?

Purpose:
To use a vector diagram to represent the changes (or lack of changes) in the horizontal and vertical components of velocity and to describe those changes (or lack of changes) over the course of time.

A complete lab write-up includes a Title, a Purpose, a Data section, a Conclusion and a Discussion of Results. The Data Section should include the provided diagrams with components of the velocity vectors drawn and labeled (vx and vy) on the diagram; the size of the vector components should be representative of their relative magnitude. The Conclusion section should use words to respond to the question raised in the Purpose section. The Discussion of Results should include answers to the provided post-lab questions.

### VP8. Projectile Problem-Solving Lab

Question:
What strategies can be used to analyze and solve a horizontally-launched projectile problem?

Purpose:
To determine and describe the appropriate strategies for solving a horizontally-launched projectile problem.

A complete lab write-up includes a Title, a Purpose, a Data section, a Conclusion/Discussion. The Data section should include the provided table with clear and thorough solutions to the three types of projectile problems. The Conclusion/Discussion section should describe in some detail the process/strategy which can be used to solve for each of the three unknown quantities. Writing should be organized, thorough and clear.

### VP9. Projectile Problem-Solving II Lab

Question:
What strategies can be used to analyze and solve an angled-launched projectile problem?

Purpose:
To determine and describe the appropriate strategies for solving an angled-launched projectile problem.

A complete lab write-up includes a Title, a Purpose, a Data section, a Conclusion/Discussion. The Data section should include the provided table with clear and thorough solutions of the three variables (ttotal, x, ypeak) associated with an angled-launched projectile problem. The Conclusion/Discussion section should describe in some detail the process/strategy which can be used to solve for the unknown quantities for such problems. Writing should be organized, thorough and clear.

### VP10. Launcher Speed Lab

Question:
What is the launch speed of the projectile launcher?

Purpose:
To determine the launch speed of the projectile launcher.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion. The Data section should include a diagram of the experimental setup with measured distances (or customary symbols for pertinent quantities) indicated on the diagram. There should be several trials of good dx data values; units should be indicated. An average dx value should be reported and subsequently used to calculate the launch speed. The calculations should be organized and clear, identifying the symbols of the variables being used in multiplication and division steps in addition to the numerical quantities. The Conclusion responds to the question raised in the Purpose (as always).

### VP11. Maximum Range Lab

Question:
How does the angle of launch effect the range of an angle-launched projectile and what angle provides for the maximum range?

Purpose:
To determine the effect of the angle of launch upon the range (i.e., the horizontal displacement) of an angle-launched projectile and to determine the angle which results in the maximum range.

A complete lab write-up includes a Title, a Purpose, a Data section, a Conclusion and a Discussion of Results. The Data section should include a table of data with labeled column headings and units. The provided graph should be included with data points accurately plotted to show range as a function of angle. The Conclusion should respond to the two questions raised in the Purpose of the lab. The Discussion of results should include theoretical predictions of range for 30Â¡, 45Â¡ and 60Â¡. Work should be clearly organized and shown. An error analysis should be included using the results of the theoretical predictions and other information from textbook readings.

### VP12. Hit the Target Lab

Question:
Given the horizontal distance from a projectile launcher to a target, at what height must the target be placed in order for the projectile to strike it?

Purpose:
To predict the height at which a target must be placed upon a vertical board a given distance from the angled launcher in order for the projectile to strike the target.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section should include a diagram of the experimental set-up with distances and angles listed upon the diagram. The launch speed (from previous lab) should be listed. A complete and organized solution to the challenge should be shown. Calculations should identify the symbols of the variables being used in multiplication and division steps in addition to the numerical quantities. A percent error analysis should be performed; work should be shown and labeled. The Conclusion/Discussion should state the predicted height and identify whether the result was successful or not.

### VP13. Hit the Target - The Sequel Lab

Question:
Given the distance from an elevated projectile launcher to the floor, at what horizontal position must a target be placed in order for a projectile to strike it?

Purpose:
To predict the location at which a target must be placed upon the floor below the launcher in order for an angle-launched projectile to strike the target.

A complete lab write-up includes a Title, a Purpose, a Data section, and a Conclusion/Discussion. The Data section should include a diagram of the experimental set-up with distances and angles listed upon the diagram. The launch speed (from previous lab) should be listed. A complete and organized solution to the challenge should be shown. Calculations should identify the symbols of the variables being used in multiplication and division steps in addition to the numerical quantities. A percent error analysis should be performed; work should be shown and labeled. The Conclusion/Discussion should state the predicted horizontal displacement and identify whether the result was successful or not.