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An Analysis of Projectile Motion Projectile Motion Lab Report PHY 302K: General Physics I (Mechanics/Heat/Sound) I. Introduction In the current unit, Unit 2.1 Two-Dimensional Motion, we have explored an applicable extension of 1-D motion as we learned in Unit 1.2 One-Dimensional Motion. By utilizing what information one is given by the situation observed, one can make conclusions based on current data collected. For instance, we can find the distance an object covered after being horizontally launched by using its horizontal speed and the altitude (height) at which it was launched from. That was an example of a horizontally launched projectile, which is a type of projectile motion; however, it is not the focus of the lab. The Projectile Motion Lab is focused on a different type of projectile motion - that of a non-horizontally launched projectile. In this type of motion, the projectile is shot at an angle, follows a parabolic trajectory, and reaches a peak height while airborne. Before diving into the lab, we needed to know what our objective entailed. Upon reading the Projectile Motion Lab handout, the group began to gather the materials we believe we needed to complete the lab as well as assign each member a role within the group to not

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Transcript of An Analysis of Projectile Motion Projectile Motion Lab Report

An Analysis of Projectile Motion Projectile Motion Lab Report PHY 302K: General Physics I (Mechanics/Heat/Sound)

I. Introduction

In the current unit, Unit 2.1 Two-Dimensional Motion, we have explored an applicable

extension of 1-D motion as we learned in Unit 1.2 One-Dimensional Motion. By utilizing what

information one is given by the situation observed, one can make conclusions based on

current data collected.

For instance, we can find the distance an object covered after being

horizontally launched by using its horizontal speed and the altitude

(height) at which it was launched from. That was an example of a

horizontally launched projectile, which is a type of projectile motion;

however, it is not the focus of the lab.

The Projectile Motion Lab is focused on a different type of

projectile motion - that of a non-horizontally launched

projectile. In this type of motion, the projectile is shot at

an angle, follows a parabolic trajectory, and reaches a

peak height while airborne.

Before diving into the lab, we needed to know what our objective entailed. Upon reading

the Projectile Motion Lab handout, the group began to gather the materials we believe we

needed to complete the lab as well as assign each member a role within the group to not

only make sure our results are as consistent as possible but that the lab runs smoothly

while optimizing the time given to complete the lab.

Needed Supplies

The team decided that to perform the lab we would require the following materials and

environment:

Nerf Gun with Foam Darts  Meter Stick  Sheet(s) of Notebook Paper and Pencil

to act as the projectile launcher and its foam dart(s)

as the projectile(s)

used to measure the placement of our markers and

to measure the distance traveled by the projectile

used to physically record the data collected before inserting

Sheet of Construction Paper  Protractor  Area free of obstacles and is at least 20 meters in length

to act as the target we want the projectile to hit

to measure the angle at which we launched the projectile

the area will be used to conduct the trials

Calculator (TI-Nspire CX)  Computer with a Spreadsheet Program (ASUS C202S

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used to determine calculations aside since Google Sheets is set to Radians rather than

Degrees

the Chromebook’s Google Sheets program was used to

organize collected data digitally as well and to provide

visuals aside from drawn models

used to mark each meter from 0 m to 20 m

Group Contributions

The group assigned each team member a role they were responsible for during the

duration of the lab. We were all given the following roles to fulfill before each were to write

their report after the completion of gathering the data necessary.

➢ Member #1

■ Organize data collected by the group and finalized data collection

➢ Member #2

■ Use the projectile launcher at a variety of angles

➢ Member #3

■ Measure the distance traveled by the projectile during each trial

➢ Member #4

■ Record all data collected during trials

II. Launch Speed

Task #1 Launch Speed is stated as the following:

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What to do: You have to determine the speed at which the projectile leaves

the launcher. You may select the materials you need from this lab from those

available. You should set the launcher to some angle of your choice. You

should launch it several times and calculate the initial velocity.

Simply, we will take the chosen materials to set up an arrangement where the projectile will

be launched from 0 meters at a constant angle the group has chosen over multiple trials.

Process

This task was the main objective of Day One. Our two main goals for the day were to prep

out “lab space” for the first and following days and to complete the first task of the lab.

Prepping the “Lab Space”

01. Mark where 0 m is located within the area chosen to perform the lab with masking

tape. On the masking tape write “0 m” with the sharpie.

02. Using the meter stick, measure one meter from where the “0 m” marker is located

at. Place a piece of masking tape where the meter ends and write “1 m” on it.

03. Measure another meter from the previous marker and label it according to how

many meters the marker is from the “0 m” marker.

04. Repeat Step 03 until you have reached your “20 m” marker. Set aside the masking

tape and sharpie.

05. We will still be utilizing the meter stick. Gather the rest of the needed supplies:

a. Protractor

b. Notebook Sheet

c. Nerf Gun with foam darts

d. Sheet of Notebook Paper

01. Lay behind the “0 m “ marker and position the projectile launcher (Nerf Gun) in the

direction of the “20 m” marker straight ahead.

02. Line up the protractor with the projectile launcher and set the launcher at the angle

desired.

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a. Note: The team decided that the angle we were going to use to launch to the

projectile was 20°

03. Once the projectile launcher is at the desired angle, launch the projectile. In this

case, you would be pulling the trigger of the Nerf Gun.

04. The team member in charge of measuring the distance traveled should measure the

distance the projectile traveled from the “0 m” marker up to the first point of impact

with the ground.

05. The team member responsible for data collection should write down the angle that

was used to launch the projectile and the distance traveled by the projectile on the

sheet of notebook paper.

06. Repeat Steps 03 - 05 at least 4 more times using the same angle chosen for the first

trial. The more trials you have, the better!

07. Clean up the lab space for the day.

08. Now, we move on to the Chromebook and the calculator. By utilizing Google Sheets

(or any other spreadsheet program) we will organize the collected information

under Day 1. This can be a section of the spreadsheet document or could simply be

its own document, separate from the data that will be collected on other days.

a. You will organize the data as such

i. Column A = Angle used to launch the projectile

ii. Column B = Distance traveled by the projectile

iii. Column C = Initial Velocity of the projectile

b. If you’ve noticed, we have not collected any data that can be considered as

initial velocity because we’ve only recorded the angle and distance traveled.

No worries! We can use the following formula to help solve for (initialiν

velocity).

09. By using your calculator and the given formula, plug in your values. Make sure that

your calculator is in Degree mode!

a. Δx = distance traveled

b. g = gravity (9.8)

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c. Θ = angle

10. Repeat the process to find the initial velocity for each trial.

11. Add all of the initial velocities calculated and divide them by the number of trials

conducted. This will give you the average velocity of the projectile (you can calculate

the average using the spreadsheet program or the calculator). Record the average

initial value in its own row/column (look at Data Collected to see the format we

used).

Data Collected

Angle (Degrees) Distance (m) Initial Velocity (m/s)

20 12.6 13.86

20 16.77 15.9899

20 16.77 15.9899

20 15.68 15.4615

20 15.07 15.1578

Average Initial Velocity: 15.29182

Analysis and Conclusion

As one can see, we have conducted five trails where we launch the projectile at an angle of

20°. Each time we launched a projectile, the projectile usually traveled a different distance

compared to the other trials. Another thing to notice is that the initial velocities calculated

for each trial do not have a large difference between them. This suggests that the initial

velocity of the projectile (on average) is near 15 m/s. Upon calculating the initial velocity on

average, we can certainly conclude that it is approximately 15 m/s.

III. Verify

Task #2 Verify is stated as the following:

Verify your launch speed. Devise some way to test your launch speed.

To elaborate, the task is to test that the launch speed (a.k.a. Initial velocity) is the “correct”

velocity of the projectile. What one would need to do here is to conduct a series of trials

using different launch values/angles in order to determine if the launch speed, or the

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projectile’s velocity, is what we determined during the first task. It would be beneficial to

conduct multiple trials and with a wide range of angles in order to acquire more “accurate:”

results.

Keep in mind that resulting numbers, in this case, initial velocities, will either vary greatly or

slightly due to the angles that are chosen to launch the projectile. It is likely that the

average velocity will differ slightly to the initial velocity average calculated in Task #1.

Process

01. Set up the lab space.

a. Set up the lab as indicated in Launch Speed: Process - Prepping the “lab

space” (look back to Task #1).

02. We will essentially be performing what was done back in Task #1; however, this time

around we will need to use a variety of launch angles. Make sure to keep in mind

what effect the launch angle has on the projectile (i.e. distance traveled).

a. Choose an angle to start the first trial.

i. You will choose a different angle for each trial and are allowed to use

the same angle no more than 3 times.

03. Once the projectile launcher is at the desired angle, launch the projectile.

04. Measure the distance the projectile traveled from the “0 m” marker up to the first

point of impact with the ground.

05. Record the angle that was used to launch the projectile and the distance traveled by

the projectile on the sheet of notebook paper (you can do this on the back of the

sheet you used for Task #1 or you can record the data on a separate sheet of paper,

but make sure you have all of your papers in order!) .

06. Repeat Steps 02 - 05 at least 9 more times. Remember: the more trials you have, the

better!

07. Clean up the lab space for the day.

08. Bring out your Chromebook and calculator.

09. Open the spreadsheet program you were using and organize all of your data in the

same format used in Task #1. As mentioned before, you can do this on a separate

sheet, separate doc, or on another section of the current spreadsheet.

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10. Calculate the initial velocity for every trial and find the average velocity. Record your

results.

Data Collection

Angle (Degrees) Distance (m) Initial Velocity (m/s)

10 8 15.1402

14 12.93 16.4289

15 13.9 16.5058

15.5 13.8 16.2044

16 13.6 15.8591

17 12.5 14.8009

19 13.98 14.9175

19.25 13.8 14.7393

19.5 14.08 14.8074

20 15 15.1225

21 14.1 14.3703

21.5 14 14.1836

21.5 14.09 14.2291

22 14.1 14.1038

25 14.9 13.8064

25 14.5 13.6198

30 15.75 13.3502

Average Initial Velocity: 14.83465882

Analysis and Conclusion

It is apparent that the team has tried a variety of launch angles throughout the execution

of the trials.The team has decided to begin with a small angle and adjust it to observe what

occurred whenever the we increased the angle measurement. Based on the data collected

and the velocities calculated, we can see that the initial velocities vary significantly.

Furthermore, the average initial velocity is near the range of 15 m/s. It is plausible that the

reason we have an average velocity slightly lower than the average velocity we calculated in

the previous task may be due to the amount of trials conducted in each task. Nevertheless,

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if we round the average velocity as we did in the previous task, we have verified that the

initial velocity is approximately 15 m/s.

IV. The Test

Task #3 The Test is stated as the following:

You will be asked to ‘hit’ a spot on a piece of paper. Your accuracy is your

In other words, by using the data collected and your observations, determine the angle you

would need to launch the projectile in order to hit a target at your desired distance.

Process

01. Set up the lab space.

a. Set up the lab as indicated in Prepping the “lab space” (look back to Task #1).

b. In addition, we will be needing a sheet of construction paper to act as a

target. Place the sheet of construction paper at the target distance. For

example, the team’s target distance was 15 m.

02. It is crucial that you have made observations on how the angle affected the distance

the projectile traveled in the previous tasks. This is where those observations and

conclusions will come in handy.

a. Set the projectile at the desired angle.

b. Launch the projectile and measure the distance traveled.

c. Record both angle and time.

d. Observe and ask yourself: did the projectile hit its target?

03. Adjust the angle or use the same angle again but do not launch the projectile at the

same angle more than three times.

04. Repeat Steps 02 - 03 a couple more times. Make sure you have conducted at least

four trials.

05. Clean the lab space entirely. We have finished executing trials for the lab.

06. Organize your data as before, calculate the initial velocity for each trial, and initial

velocity on average. In addition, add another column with the target’s distance.

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Data Collection

Angle (Degrees) Distance (m) Initial Velocity (m/s) Target Distance (m)

19 15 15.4521 15

20 15.32 15.283 15

20 15.08 15.1628 15

20 15 15.1225 15

20.5 15 14.9688 15

Average Initial Velocity: 15.19784

Analysis and Conclusion

Based on the data we have seen in our previous trials prior to Task #3, the team has

determined that the “sweet spot” to hitting the desired target is around 20°. The team

members concluded that to hit the target that is 15 meters from the “0 m” marker we

should adjust the launch angle to an angle that does not stray far from 20°. Once we have

completed our trials, our initial velocities and average initial velocity were approximately 15

m/s. Furthermore, in all of our trials, the projectile hit the desired target.

V. Uncertainty Analysis

Analysis and Conclusion

There were many factors that could have affected how “true” our data and calculations.

Some of these factors may just be small things, but may have had a monumental effect on

the results from the lab. Without knowing what specifically caused the lab produce

accurate and truly “true” results, we can only account the possible factors as we tried to

gather data and execute trials that are as accurate a possible. Here are two examples of

what could have affected the results from the lab.

Projectile Change

Throughout the course of the three days we have completed the three tasks, we

shared our projectile launchers with other groups and other classes. It is very likely

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that the projectiles were mixed up between uses and since many are identical (all

had a flat tip and were either of blue or yellow color), thus it’s most likely true that

we did not use the same projectile throughout the lab.

Inaccurately Measured Distance

The human eye cannot always calculate exact movements within our surroundings

due to the flow of information from our surroundings to our eyes and to our brains.

With that being said, it is a certainty that when we measured the distance after the

projectile first hit the ground, the distance measured was an estimate since we do

not accurately know where the projectile first touched the ground.

VI. Experiment Summary

In general, this lab was to see the relationship between the projectile’s launch angle,

distance traveled, and initial velocity. In this lab, we had to accomplish 3 tasks:

- Find the initial velocity of the projectile

- Verify the initial velocity

- Using the data from the other tasks, launch a projectile to hit a target

We used the materials chosen (see material list under Introduction: Needed Supplies) to

create a lab space that can provide the necessary results to draw conclusions from and that

can accomplish the given tasks. For the first task, the group launched a projectile at an

angle of 20° five times in order to calculate the initial velocity. During the second task, the

team executed multiple trials in order to confirm the initial velocity and to formulate an

idea of how the angle at which the projectile was launched affect the distance traveled by

said projectile. For the final task, the group launched a projectile at angles near 20° in order

to hit the target that is approximately 15 m from the “0 m” marker.

The group few minor challenges throughout the lab. Out most noticeable challenge was

near the beginning of the lab. The group had a general idea of how were were to approach

the execution of the given tasks, but did not have a specific process during the first few

trials. However, when the group came together before the completion of the first task, the

group discussed a detailed plan of action to follow in order to complete the lab.

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VII. Conceptual Connections

No experiment is perfect – there is always room for improvement!

I have noticed that there are a few things that the group can improve if we were to conduct

this lab at another time.

- For example, if we were given more time (either in class or throughout the week)

rather than stretching the lab over the course of three days, the team could have

conducted more trials.

- And speaking of trials, the team could also conduct an equal amount of trials for all

three tasks rather than have five trials for the first task, 17 for the second, and five

for the third.

- Since the projectile change between trials is considered as a potential factor for

uncertainty, the team, if we were to conduct the experiment again, would use the

same projectile throughout.

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