PHYS 250 CC Projectile Motion Questions

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PHYS 250

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Physics 250: Projectile Motion Objective: Study the relationship between height, initial velocity, initial angle and range of the object in twodimensional projectile motion. To find the simulation go directly to this link: http://phet.colorado.edu/en/simulation/projectilemotion Click “Intro.” When the simulation opens, hit the “Fire” button. Spend 5 minutes just playing with the simulation to see what it can do. Finding g: Use these settings: an angle of 60° and an initial speed of 18 m/s. Come up with a strategy to verify what value the simulation is using for g. You can use the measurement tool on the top right part of the screen and move it to any point on the projectile and measure the time, horizontal or vertical position of the object. Describe your strategy here including the equations and calculations here. page 1 Predict: What will happen to the range when you double the velocity? Now change the mode to “Lab” mode and do the rest of the lab in this mode. Horizontal distance versus initial speed: Experiment 1 (Keep the height at 10 m): objective: How initial speed affects the range of the projectile while keeping the height constant. Set the angle to 60 degrees. Find the range for several different values of initial speed (make sure you get values over the whole range of initial speeds available). Make the following table in Excel and plot the graph of Horizontal distance vs. vi. Is there a linear relationship between the variables? In the next step add another column to your table and label it as vi2. Now, plot the graph of Horizontal distance vs. vi2. Is that graph linear? What you can conclude about the relationship between initial velocity and horizontal distance? vi (m/s) 8 10 Horizontal distance (m) vi2 (m/s)2 15 19 25 27 30 Were you correct in your prediction? Explain. page 2 Maximum range in same level projectile: + Reduce the height of the cannon to be zero by clicking on the sign on cannon and lower it down so that the height reads 0 m. Predict what initial angle will produce maximum range (range is the total horizontal distance traveled by the projectile), in the case when the projectile lands at the same level it was launched from. What is your predicted value of the initial angle? ______ Range versus launch angle (Same level Projectile): Experiment 2: keep vi to be constant and create the below table in the Excel. Fill the table for several values of θ and range. Again, get values from the whole range of angles available to you. You can use the measurement tool – place it on the impact point to read the range, height, and time for the projectile. Plot the graph of Range vs. angle in Excel. θ(deg.) (x-axis) Range (m) (y-axis) Was your prediction correct? Explain. page 3 Derive Range Equation: Now you’re going to find an equation for the range (defined as the x displacement of the projectile when it reaches y=0) for a cannon firing from y=0. Leave everything as variables, such as vi for the initial velocity, and θ for the launch angle. 1. Write out an equation that gives the horizontal position of the object in terms of vix and time. 2. Solve your equation from question 1 for time. ∆t = ................................ (equ. 1) 3. Write out the equation of the vertical displacement of the object (Δy) in terms of viy, g, and time. Choose down to be negative. ∆ y = ................................ (equ. 2) 4. Substitute your equation 1 into your equation in 2, which should produce what we call the range equation – an equation that tells you how far horizontally the object travels, in terms of vi and θ. Solve your equation from question 2 for Δx. You may find the following relation useful: 2 sinθcosθ = sin(2θ). 5. In particular, how does the range depend on vi ? Does this match your results from the experiment 1? Why? Assessment: Once you have completed this part, choose 3 sets of the angles and initial speeds of the cannon. Using the equation you derived in the previous step, move the target so that the projectile hits it on the first try. θ1 = v1i = θ2 = v2i = θ3 = v3i = Did you succeed? [ ] Yes [ ] No If not, what went wrong? Did you succeed? [ ] Yes [ ] No If not, what went wrong? Did you succeed? [ ] Yes [ ] No If not, what went wrong? page 4 Horizontal projectile: Experiment 3: Varying Launch Height: Now, re-set the cannon so that it launches projectiles from a large height. Move the cannon to the height of 12 m and then set the launch angle to 0°, so the projectile is launched horizontally with initial velocity of 18 m/s. The simulation should now look something like this: Using the measurement tool: Measure the horizontal distance from the origin to the target: ____________ Record the height of the cannon: ____________ (unit) (unit) Now, with the launch angle at 0°, predict what the initial speed should be so that the projectile hits the target. Show your work for this prediction here: page 5 Check your prediction with the other members of your group. Come up with a group consensus on the value of the initial speed that will allow the projectile to hit the target. What is your group predicted value? _______ Now run the experiment. Did you successfully hit the target? [ ] Yes [ ] No If not, repeat the process until you successfully predict a value of the initial velocity that will allow you to hit the target. page 6
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Explanation & Answer

Please view explanation and answer below.Hi, here the second experiment alone.

Physics 250: Projectile Motion
Objective:
Study the relationship between height, initial velocity, initial angle and range of the object in twodimensional projectile motion.

To find the simulation go directly to this link: http://phet.colorado.edu/en/simulation/projectilemotion

Click “Intro.” When the simulation opens, hit the “Fire” button. Spend 5 minutes just playing with
the simulation to see what it can do.

Finding g: Use these settings:

an angle of 60° and an initial speed of 18 m/s. Come up with a
strategy to verify what value the simulation is using for g. You can use the measurement tool on the
top right part of the screen and move it to any point on the projectile and measure the time,
horizontal or vertical position of the object. Describe your strategy here including the equations
and calculations here.

page 1

Predict: What will happen to the range when you double the velocity?

Now change the mode to “Lab” mode and do the rest of the lab in this mode.
Horizontal distance versus initial speed:
Experiment 1 (Keep the height at 10 m):
objective: How initial speed affects the range of the projectile while keeping the height constant.

Set the angle to 60 degrees. Find the range for several different values of initial speed (make sure
you get values over the whole range of initial speeds available). Make the following table in Excel and
plot the graph of Horizontal distance vs. vi. Is there a linear relationship between the variables?
In the next step add another column to your table and label it as vi2. Now, plot the graph of
Horizontal distance vs. vi2. Is that graph linear? What you can conclude about the relationship
between initial velocity and horizontal distance?

vi (m/s)
8

10

Horizontal
distance (m)
9.2

vi2 (m/s)2
64

12.81

100

15

24.54

225

19

36.04

361

25

60.45

625

27

69.69

729

30

84.86

900

Were you correct in your prediction? Explain.

page 2

Maximum range in same level projectile:

+

Reduce the height of the cannon to be zero by clicking on the sign on cannon and lower it down
so that the height reads 0 m. Predict what initial angle will produce maximum range (range is the
total horizontal distance traveled by the projectile), in the case when the projectile lands at the
same level it was launched from.
45º
What is your predicted value of the initial angle? ______

Range versus launch angle (Same level Projectile):
Experiment 2: keep vi to be constant and create the below table in the Excel. Fill the table for
several values of θ and range. Again, get values from the whole range of angles available to you. You
can use the measurement tool – place it on the impact point to read the range, height, and time for
the projectile. Plot the graph of Range vs. angle in Excel.
θ(deg.)
(x-axi...


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