NORTHERN ILLINOIS UNIVERSITY
PHYSICS DEPARTMENT
Physics 253 – Fundamental Physics Mechanics
Lab #3 – Projectile Motion
Meet in FR 233.
Sections A, B, C, G: Tuesday Sep. 13; Sections D, E, T: Thursday Sep. 15.
Read Giancoli: Chapter 3
Lab Write-up due Tue. Sep. 20 (Sections A, B, C, G); Thur. Sep. 22 (Sections D, T)
Experimental setup: The ball is shown as a blue circle
Figure 1
Apparatus
This experiment uses two different methods to launch a ball horizontally. Both
use gravity to get the ball rolling, and a straight section to launch the ball. A long tube
will be used in Part A to find the range of the ball. A short launching ramp will be used
in Part B to find the trajectory of the ball.
In Part A the end of the long tube is a height h above the ground. The ball comes
out of the tube with an initial horizontal velocity v0x. As the ball flies through the air it
will curve downward due to gravity and strike the floor some distance R away from the
end of the tube.
In Part B the path of the ball can be measured with a vertical board covered with
carbon paper. The board can be placed at various distances x away from the end of the
tube. The impact of the ball on carbon paper leaves a mark that can be transferred to the
graph paper attached to the apparatus. The sequence of marks on the graph paper
represents the vertical position y of the ball at different points in its flight.
Theory
The ball comes out of either tube in the direction of the last section of the tube.
This direction is purely horizontal at some initial velocity v 0x . This velocity can be
measured by finding the time t that it takes to go between two points in the horizontal
tube separated by a distance D . The velocity is then
D
(1)
v 0x 
t
A projectile in the air is subject to acceleration ay  g downward due to Earth’s
gravity. The constant g=9.8 m/sec2 is the acceleration due to gravity. The acceleration

only acts downward and has no effect on the horizontal motion. Since there is no initial
vertical motion for the ball, the distance downward is given by

1 2
y  h  gt
(2)
2
where h is the initial height.
The time it takes the ball to hit the ground is found by setting y=0 (the ground)
and solving Eq. 2 for t :
2h
t
(3)
g
There is no acceleration in the horizontal direction so the forward distance covered when
the ball hits the ground, called the range R, is found by substituting the time from Eq. 3
into the expression for distance: x  v0x t (since xo=0 and ax=0 ). Thus, when the ball hits

the ground,
2h
R  v 0x
(4)
g

A similar set of equations applies to the motion of a projectile before it reaches the
1
ground. The vertical distance down from the starting point is y  h  gt 2 and the
2

horizontal distance is x  v0x t . If these two equations are combined to eliminate t , then
we get
g
(5)
y  h  2 x2

2v 0x

This equation describes the trajectory of the projectile.

Data Collection
When doing measurements, alternate between lab partners for each measurement—no
lab partner should do all the measurements. This reduces any possible measurement
bias.
Part A: Long Glass Tube
(1) Measure the height of the long tube above the floor. This is the vertical distance h
that the ball will fall.
(2) Use a timer to determine how long it takes the ball to travel the distance between two
marks separated by one meter while in the tube. Repeat your timing five times, (a
different lab partner should perform successive time measurements) recording each
time, and take an average to use as the time t .
(3) Calculate the horizontal speeds (five of them) of the ball v 0x in the long level portion
of the tube with D  1 m, using Eq. 1.
(4) Use the height h and horizontal speed v 0x to predict how far out from the spot on the
(5)
(6)
(7)
(8)
floor directly beneath the opening of the tube the ball will land, using Eq. 4. This is
the range R .
Test your prediction by taping some carbon paper on top of a plain sheet of paper to
the floor where you expect the ball to hit. Send the ball through the tube ten times
letting it hit the paper each time to make a mark on the carbon paper (let each lab
partner do this at least twice).
Measure the horizontal distance from the spot on the floor directly beneath the
opening to the edge of the paper.
Measure and record the distance of each mark on the paper from the edge of the paper
and find an average.
Add the average distance on the paper to the distance of the paper from the tube along
the floor to get the measured range.
Part B: Trajectory Apparatus
(1) Adjust the angle of the launch ramp so the short section is horizontal. Leveling the
launch ramp can be done with the bubble level or by placing the steel ball on this
section of the ramp and adjusting the angle until the ball rests in one place.
(2) Release the small metal ball from several positions on the launch ramp and watch its
path after it leaves the ramp; see how it curves downward. Do this a few times.
(3) Tape a single sheet of graph paper against the plotter board. The steel ball will trace
a path across the paper beginning somewhere at the upper right corner of the grid.
This means that the right hand side of the graph paper must be even with the end of
the launch ramp. Make a mark on this edge even with the center of the ball when the
ball is on the end of the track. Tape the upper right corner of the paper to the plotter
board. Make sure the horizontal lines on the paper are parallel to the top edge of the
plotting board, then tape the remaining edges of the graph paper to the plotter board.
(4) Measure the height of the end of the launch ramp above the bottom of the graph
paper. This is the starting value of the vertical distance h.
(5) Tape a strip of recording paper to the surface of the target plate. The paper should be
smooth and tight. This will record the locations where the ball impacts the target
plate. Position the target plate 2 to 3 centimeters from the end of the launching ramp.
The target plate should be aligned vertically with the graph paper grid.
(6) Release the ball several times from the stop on the ramp and transfer the marks on the
paper taped to the target plate onto the graph paper by holding an index card against
the target plate at the level of the impact mark and squarely against the graph paper.
Make a small dot on the graph paper where the corner of the note card and the graph
paper meet.
(7) Repeat Step 5 several times positioning the target plate 2 to 3 centimeters farther
from the end of the launch ramp each time.
(8) Next to each mark on the graph paper record the horizontal distance x from the edge
of the paper and the vertical height y from the bottom of the paper.
(9) Record this data into a table of x vs. y coordinates.
(10) Draw a smooth curve through the data points on the graph paper in your lab
notebook and label the graph vertical distance y vs. horizontal distance x . Show
this plot to your lab TA. Notice that the graph has no time axis; only distance units
(cm) are used. Your graph illustrates the trajectory of the ball.
Data Analysis and Discussion
(1) Part A: Why did you take five measurements of the time with the long tube? How
did the first time measurement compare with the average time?
(2) Part A: Compare your predicted range to the distance you just found experimentally.
How good was your prediction? How close would your prediction be if you only used
the first trial?
(3) Part A: What effects might account for the different positions of the marks?
(4) Part B: From your graph in Part B (9), estimate the value of R by extrapolating your
curve down to y  0 . Do the extrapolation by hand, where you continue drawing
what you expect the curve to do down to y  0 . What value do you get?
(5) Part B: Using Excel, plot the theoretical curve of the trajectory given by Eq. 5 and
your experimental data on the same graph (use Eq. 4 and your range R to determine
v 0x ). Is there good agreement between theory and experiment? Discuss what may
cause any discrepancies. Fit your data with a parabola (polynomial of order 2) using
Excel. The results of the fit correspond to the coefficients in Equation 5, which can
be solved for the velocity and height. What value does your fit give for the initial
velocity of the ball as it leaves the tube, v 0x , and the height, h ? Are these reasonable
values?
(6) Part B: How accurately were you able to measure the horizontal position? How
would this contribute to any differences in the trajectory?
(7) Part B: How does a graph depicting the trajectory differ from a graph of position
versus time?