Projectile Simulation

Purpose:  1. To gain a better understanding of motion in two dimensions by working a projectile
problem
   2.  To gain experience using a computer simulation of a physical problem
Equipment Needed: windows based computer with Interactive Physics software
Introduction: The computer will be used to create a simulation of a rubber ball being thrown through a
window on the side of a building.   The computer, of course, uses the laws of physics
(previously programmed into the computer) to simulate the motion.  In a similar way, we
can use the laws of physics to do the calculations ourselves and predict the correct initial
velocity needed and thus check the accuracy of our simulation.  The only other means of
verifying any simulation (and the best!) is doing the actual experiment, but depending on
the situation this may be difficult and/or costly.
By adjusting the initial velocity of the ball we can use the computer to repeat the
experiment over and over again until we achieve the desired result (getting the ball
through the window).  The ball's initial velocity is controlled by using the slider bars for
Vx and Vy or by simply typing in values in the boxes below each slider.  Be sure that the
simulation has been reset before making any changes.  The components, Vx and Vy, of
the ball's velocity are displayed by digital meters.  Vectors attached to the ball indicate
the ball's velocity as well as the x and y components of the velocity.
Procedure:
1.  Turn on the computer and load the Interactive Physics software located within the Physics Apps
folder.  Select File/Open and double click on FLYBALL file.
2.  Set the initial velocity of the ball by adjusting the sliders for Vx and Vy and observe the initial
velocity vector attached to the ball change as you adjust the sliders.  Run the simulation and observe
the motion of the ball.  Watch the velocity vector and its components as they change throughout the
motion.
Repeat the simulation with a different initial velocity until the ball goes through the center of the
window.  Record V0x, V0y, and the total elapsed time.  Also locate the initial position of the ball by
moving the mouse until the cursor on the center of the ball.  Read the values for x and y in the
coordinate boxes in the lower left portion of the screen.  In a similar manner, determine the
coordinates of the center of the window.   Make a motion diagram showing all relevant variables.
Using your motion equations, calculate what the time of flight should be and compare with the
simulation time.
V0x
V0y
∆t
x0
y0
xf
 
yf3.  Using the player controls, step the motion back to where your projectile is at the very top of its path.
Record the values for Vx, Vy, and t at this point.  From your initial velocity, calculate what the time
should be at the top.  How does your calculated time compare with the simulation’s time?
4.  Run the simulation using a ball speed of V0x = 6.00 m/s and V0y = 8.02 m/s.  Record the horizontal
and vertical components of the velocity at various times (using the player controls), completing a
table like the one shown below.  Be careful to record the sign (positive or negative) in all cases.
Time (s) Vx (m/s) Vy (m/s)
0.0 6.0 8.02
0.2
0.4
0.6
0.8
1.0
1.2
1.4
5.  Using the data from the table, plot the horizontal and vertical components of the velocity, Vx and Vy,
versus time on a single graph in Graphical Analysis.  Use different symbols to mark the data points
for the two velocity components. You should observe that one component of velocity changes while
the other is constant.  Explain.  What should the slope for each curve be?
6.  Fit the graphs and find the slopes of the lines.  Did they agree with your expectations?  Explain.
Print a copy of the graphs for everyone in the group.    7.  The horizontal and vertical positions of a projectile in free fall are given by
x = x0 + V0xt + ½axt
2
y = y0 + V0yt +  ½ayt
2
Solve each of these equations algebraically for V0x and V0y.  
8.  Using the results from part 7, calculate V0x and V0y
for a time of flight of 1.6 s and then run the
simulation.  Verify that the ball does go through the center of the window for your calculated values
of V0x and V0y .  Repeat for a time of flight of 1.33 s and  0.5 s.  Sketch the shape of each trajectory
and discuss the differences in the trajectories.  What determines the amount of time the projectile
spends in the air?
9.  Calculate the initial speed (magnitude of the velocity) and direction (angle above the horizontal) for
each of the three simulations discussed in part 8.  Put the results from parts 8 and 9 in a table.
    V0      θ

Conclusions:

The purpose of the projectile simulation lab was to estimate the trajectory an object would take to undergo a predetermined behavior and by mechanics of kinematics, we were to ascertain the velcocities of the x and y directions to make the object fulfil the desired behavior given initial and final positions as well as acceleration. Before this lab, I was completely confused as to how a
"split-up" kinematic equations were related and afterward I was able to relate them by solving for certain variables and interpolating them into the other equation, much like one of the rocket problems discussed during the course of the semester.