Simulating Projectile Motion
Answer questions and use track changes to submit electronically.
Looking at Components
1. Open Safari and go to this website:
http://www.mhhe.com/physsci/physical/giambattista/proj/projectile.html. (note there is a link
on the webpage for this chapter).
2. Make sure the applet is set to the biker and side view. Clicking play will get the biker
moving. You can reset the motion and then view it in slow motion by adjusting the
Simulation Speed slider. You can also step through the simulation if needed.
3. Adjust the controls until you get the biker to land safely on the pillows. You will get a You
Did It message when this occurs.
4. Turn on the velocity vectors. Run the simulation until the biker reaches the peak of flight.
5. What is happening to the magnitude of the y component of the velocity on the way up?
6. What is happening to the magnitude of the x component of the velocity on the way up?
Continue running the simulation until the biker lands.
7. What is happening to the magnitude of the y component of the velocity on the way down?
8. What is happening to the magnitude of the x component of the velocity on the way down?
Turn on the acceleration vectors. Run the simulation.
9. What is the value of the horizontal acceleration throughout the flight?
10. What happens to the vertical acceleration throughout the flight?
11. When does the vertical velocity become zero?
12. When does the vertical acceleration become zero?
Change the View of the simulation to a top view. Run the simulation with the velocity vectors
on.
13. What happens to the velocity during the flight?
14. Notice the dots being left at even time increments. Describe the spacing. What does this
indicate about the motion shown?
Change the View of the simulation to a front view. Run the simulation.
15. What happens to the velocity during the flight?
16. Describe the spacing of the dots this time. What does this indicate about the motion shown?
17. Which view is being shown: horizontal or vertical?
Solving Problems
1. Open Safari and go to this website:
http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapp
let.html (note there is a link on the webpage for this chapter).
2. The ball has an adjustable initial speed and can be launched at an adjustable angle. After
firing the projectile, the applet will list the maximum distance, maximum height, time of
flight and final velocity.
3. Set the initial velocity to 36 m/s and the angle to 45°. What is the time of flight from the
applet?
4. Calculate the time of flight from the values of the initial speed and the angle. How does
your answer compare to the applet?
5. Set the initial speed to 50 m/s and try both 30° and 60° angles. What do you find?
6. Can you get this to occur for other sets of angles? What is the relationship between the
angles when the range is equal?
7. Set the initial speed to 40 m/s and run the simulation for different angles. Record the
angle, range (x distance) and time of flight in an Excel spreadsheet.
8. Graph time vs initial angle. What does the graph indicate (in other words what does the
relationship appear to be)? Is the graph symmetric about some point?
9. Graph range vs initial angle. What does the graph indicate? Is the graph symmetric about
some point? Print both graphs on one page.
10. Go back to the simulation. Run the simulation both with and without air resistance. Try this
for different angles and speeds. What conclusions can you draw as to how air resistance affects
the path of a projectile?
Questions:
1. Is the velocity at the top of the flight zero?
2. For a given initial speed, how does the angle affect the time of flight?
3. For a given initial speed, how does the angle affect the range?
Graphing Projectile Motion
Open Safari and go to this website: http://www.walter-fendt.de/ph14e/projectile.htm.
Set the simulation to the following values: initial height = 10.0 m, initial speed = 20 m/s, initial
angle to 45°. Turn on slow motion.
Open Excel and create a worksheet with the following quantities: time, horizontal position,
vertical position, horizontal velocity, and vertical velocity.
Run the simulation and then pause it. Record the values into the table. To get the distances click
on the Coordinates button. Click on velocity to get those values.
Click resume and then pause the simulation and record values. Repeat this for at least 10 points.
Make sure you have values from throughout the motion from launch to landing.
Use Excel to create the following graphs: X vs time, Y vs time, vx vs time and vy vs time.
Apply trendlines to each of the graphs. Copy and paste them in Word so they will print on 1
page. Below each graph, type in the equation you think matches the motion. Then indicate what
each number in the equation represents.
1. X vs time. What is the shape? What type of motion does this indicate is occurring? What
does the slope represent?
2. Sketch the XT graph below. In other color (or dotted line), how would the graph change if
the angle were greater?
3. Y vs time. What is the shape? What type of motion does this indicate is occurring?
4. Does the object begin returning towards its starting position? How do you know based on
the Y graph?
5. Sketch the YT graph below. In other color (or dotted line), how would the graph change if
the initial position were greater? What if the angle were less?
6.
vx vs time. What is the shape? What type of motion does this indicate is occurring? What
does the slope represent?
7. Sketch the VxT graph below. In other color (or dotted line), how would the graph change if
the initial velocity were greater? If the angle were less?
8. vy vs time. What is the shape? What type of motion does this indicate is occurring? What
does the slope represent?
9. Does the object begin returning towards its starting position? How do you know based on
the vy graph?
10. Sketch the VyT graph below. In other color (or dotted line), how would the graph change if
the initial position were greater? If the angle were greater?