**Objectives:**

- Students will predict kinematic information for various situations on a projectile motion virtual simulation
- Students will analyze and recognize patterns and trends in the data that they gather during this activity
- Students will apply concepts previously developed about vectors and trigonometry to the concepts of projectile motion.

**Set-Up**

- Use the following link to open the “Projectile Motion” Phet Simulation:
- When the lab opens, you will arrive at this screen:

Click around and get acclimated with the controls as you need to. We have played with this simulation before, so it should be somewhat familiar, but click on the buttons and fiddle with the controls as you see fit.

- For planning purposes, we will be keeping gravity constant in this lab at 9.81 m/s
^{2}which is the acceleration due to gravity of the Earth. The mass and diameter of the object will also be kept constant for this lab. You may set those as you see fit or choose from one of the preset items from the drop down menu on the side (for some added chuckles). - When you comfortable enough with the controls, click on the “Lab” option to begin the lab. You will work on this option for the remainder of the lab

**Part I: Horizontally Launched Projectiles**

Fill in the table below as you find the different values in this part of the lab.

| | 0 | | |

- Set the initial height of the cannon to 10 m, its initial speed to 18 m/s and the angle of the cannon to be exactly 0
^{o }as per the screenshot below:

- For a situation like the one above, what is the initial, vertical velocity ( ) of the projectile be? Explain your answer either qualitatively or quantitatively (or both) in the space below:

-The projectile will be at rest. Thus the initial, vertical velocity is 0.

- Once the cannon fires its projectile, does the horizontal velocity of the projectile increase, decrease or stay constant over time? How do you know? Explain your answer in the space below.

- Using kinematic equations, predict how far away from the cannon, horizontally the ball will land. Use the space below to show your work.

X=V(T)

- See if your prediction was correct by firing the cannon. Take a screenshot of your successful shot in the space below.

*(at this point, you should have both t and* * filled in on the first table)*

- In the space below, calculate the final vertical velocity ( ) of the projectile

- At this point you now know information about both the horizontal and the vertical components of the projectile’s velocity. In the space below, draw a diagram of the vector components of and using tip-to-tail method.

- To the diagram that you drew above, draw in the resultant vector, and the angle, .
- Using your knowledge of vectors and trigonometry, in the space below, calculate and .

*(at this point, the rest of table at the beginning of this section can be filled out)*

- Using words, describe the trajectory of a horizontally launched projectile. How do the kinematic values change over time in the horizontal (x) dimension? How do the kinematic values change over in the vertical (y) dimension? What did this actually look like when the projectile was fired? Why do you think the trajectory looks the way that it does?

- Reflect on the math and equations that you used to determine the horizontal displacement ( of the projectile. Summarize, in words, the process you used to find the horizontal displacement of the object in an organized and logical manner.

**Part II: Projectile Launched at an Angle**

Fill in the table below as you find the different values in this part of the lab.

- Keep the target at the same location on the ground from the end of the previous section of the lab, but lower the height of the cannon all the way down to 0 m, as in the picture below:

- Let’s try to hit the target again now from this height. Change the angle of the cannon and the initial speed as you need to so that when the cannon is fired, the projectile strikes the target. Paste a screenshot in the space below when you successfully hit the target.

*(at this point you should be able to fill out* *and* * in the table for this section of the lab)*

- What is different about the initial speed in this part of the lab compared to the last part of the lab. Apply concepts of vectors and trigonometry in your explanation.

- Using trigonometry, resolve the initial speed of the projectile into horizontal (x) and vertical (y) components. Show your work in the space below.

- Use the tools at the top of the simulation to measure both the horizontal displacement of the ball and the time the ball spends in the air. Record these values in the table at the beginning of this section

- Find the horizontal velocity ( ) and the initial vertical velocity ( of the projectile using the kinematics equations. Show your work in the space below.

- How do these values compare to the values you calculated in Question 15? What conclusions can you draw from this pattern?

*(at this point you should be able to fill out* * * * and* * in the table above)*

- Describe the trajectory of the object, qualitatively. How does this trajectory compare to that of a horizontally launched projectile?

- How does the velocity change as a vector over time? Describe both the original vector and its components as they change over time. (Note: Think of this question not just in terms of number, but also in terms of the orientation of the velocity vector of the projectile).

- Using the Kinematics equations, determine the maximum height that the projectile reaches in its trajectory. Show all of your work in the space below. Then use the measurement tools in the simulation to confirm your calculations. Paste a screenshot of your measurement next to your work in the space below.

*(you should have the entire table filled out at the beginning of this part of the lab).*

**Part III: Projectile Launched at an Angle with an Initial Height**

Fill in the table below as you find the different values for this part of the lab

- Keep both the initial speed and the angle of the cannon the same from the previous section of the lab, but now raise the height of the cannon to 7 m as shown in the screenshot below:

- The first goal for this part of the lab is to predict the horizontal range of the projectile. Using the equation , to set up the equation to find the hang time of the projectile by plugging the known values into the equation. What do you notice about this equation, compared to the other times we have use this when calculating time?

- You will need the quadratic formula to solve the equation from the previous step. If you know the quadratic formula from memory, copy it down here. If you do not know the quadratic formula, then you may need to look it up and define for yourself what each of the variables mean in order to use it correctly.

- Use the quadratic formula to find the hang time of the ball. You may find that you have two solutions when you use the quadratic formula correctly. Are the two solutions legitimate? Why or why not? Which of the two “times” that you calculated from the quadratic formula should you use to move forward with finding the horizontal range of the projectile? Justify your reasoning for your choice.

- Using the time you chose in the previous step, predict the horizontal range of the projectile using the kinematic equations in the space below.

- Test your prediction by firing the cannon and seeing where your projectile lands. When you successfully hit the target, paste a screenshot of your successful trial in the space below.

*(you should be able to fill out t and* * in the table at the beginning of this part of the lab at this point)*

- Using the kinematics of the scenario, calculate , the final velocity of the projectile and , the angle at which the projectile strikes the ground at. Show your work in the space below and be sure to include a diagram of the components of .

- Using the kinematics of the scenario, calculate the maximum height, , that the projectile attains in its trajectory. Show all of your work in the space below. When you have an answer, use the measurement tools in the simulation to confirm your calculations and paste a screenshot in the space below.

*(you should be able to fill out the rest of the table for this section of the lab at this point)*

- Final Challenge: We have done a TON of kinematics and projectile motion practice with this lab. With this final prompt, play with any of the settings that we have not yet played around with on this lab (gravity, air resistance, size of the object or mass of the object). How does changing the parameter that you messed with impact the kinematics, the math and the trajectory of the object? Was it the same? Did something change? If something was different, what changed. Paste Screenshots or sample calculations in the space below.

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