For motion in 2 dimensions we can calculate components of velocity and
acceleration by differentiating x and y as functions of time. We can then
use Pythagorean Theory to get the total value
PROJECTILE MOTION
SoftBall Projectile Some Observations
So far we have been dealing with horizontal motion along a straight
line and vertical motion along a straight line separately. Here we would
like to study motions in a plane such as the motion of a thrown softball
or the circular orbit of a satellite.
If a softball is thrown off a cliff with a certain initial velocity
in the xdirection and ydirection, it will continue to move forward in
the x direction and at the same time fall in the ydirection as a result
of the attraction between the earth and the ball. The twodimensional motion
that a result is known as projectile motion.
Why is it that the projectile keeps the same horizontal velocity?
JienTze Drop and Kick
NAME ____________________________ PARTNER ________________________ DATE
_______
PURPOSE
This activity or lab investigates the use of vectors to solve physics
problems with the use of a Traditional Taiwanese Toy (JienTze) and a variety
of other materials available.
MATERIALS
Assorted JienTze, assorted balls or other materials chosen by students,
timing devices, and measurement devices.
Situation A
Karen and Sarah find some JienTze toys near the edge of a cliff in
the local park. They know they can calculate the height of the cliff by
finding the time it takes the JienTze to fall to the ground and then using
the formula d = 1/2gt2. They wonder if the formula will work for a JienTze
kicked off the cliff instead of dropped straight down over the edge. Karen
and Sarah design an experiment to find the answer. Karen drops one JienTze
over the edge at the exact moment Sarah kicks the other JienTze off the
cliff.
Make a Prediction
1. Predict which JienTze will hit the ground first  the JienTze dropped
over the edge or the JienTze kicked outward off the cliff. Assume there
is no air resistance.
Design a method or experimental procedure to confirm or refute your
prediction:
2. List the forces acting on each JienTze as it falls. In which direction,
x or y, do these forces act?
3. Was your prediction correct? Explain the results in terms of the
force vectors acting on each
JienTze.
4. How do the vertical positions of the falling JienTze compare?
5. Using the results of the experimentation and the formula d = 1/2agt2
, calculate the height of the cliff (balcony) you used (ag = 10.00 m/s2).
Situation B
Karen and Sarah now decide to investigate what will happen when one
JienTze is thrown vertically upward while the other is kicked upward and
outward. Assume both the JienTze have the same initial vertical velocity.
Make a Prediction
6. Predict which JienTze will hit the ground first  the JienTze thrown
upward or the JienTze
kicked upward and outward. Assume there is no air resistance.
Design a method or experimental procedure to confirm or refute your
prediction:
7. Was your prediction correct? Explain the results in terms of the
force vectors acting on each JienTze.
8. Explain what happens to the Force of gravity vector as the JienTze
fall.
9. Describe what happens to the Velocity vector for each of the JienTze
as they fall. Explain why the Velocity vector for the kicked JienTze changes
magnitude and direction during the fall.
JienTze PROJECTILE METHOD (Formal Lab
Report)
OBJECTIVE
To determine the range of a projectile as a function of projection angle.
MATERIALS
Projectile firing apparatus for use with a JienTze, meter stick or
tape measure.
PROCEDURE
STEP 1 Finding the speed of the JienTze
 You probably should do this experiment outdoors (if the weather is
cooperative) so that the projectile doesn't hit anything (actually the
JienTze won't harm a thing, it's just a nice opportunity to get outside);
otherwise an empty hallway may be adequate. Set the firing apparatus on
a table or flat surface in such a way that it can be fired at an angle
0o relative to the horizontal. Aim the projectile where it won't hit someone
or something. At some angles it will have a range of around 5 meters and
a maximum height of nearly 3 meters.
y = yo + vo sin q t  1/2 agt2 x = xo + vo cos q t
use yo = height then when it hits the ground y = 0
use xo = 0
 Measure the height of the JienTze from the floor. Shoot the JienTze
at 0o several times; use the range, X position when it hits the ground,
to find the initial speed of the JienTze.
STEP2 Projected at Same Height as Lands: Measuring Range
 After you have found the initial velocity of the projectile using the
table and zero degrees, you will shoot the projectile from ground level
and use a box or a few books so that it lands at the same altitude it was
shot; yo = yf = 0. Place a piece of tape at the expected impact point,
then run two or three trials for each angle in a chart like the one below.
Do this for each of the angles (but not zero degrees). Station a lab partner
near where the projectile strikes the box. He is to measure the average
range of the two or three trials. Measure the average range for each angle
of projection and record the data.
STEP3 Projected at Same Height as Lands: Calculating Range
 If you have taken trigonometry, using Trig identities you should be
able to show that the range is
. Use the initial velocity, vo, from procedure 2 above at zero degrees
in all your calculations and fill in the Theoretical Displacement in your
chart.
Angle 
Net Vertical Displacement 
Theoretical Horizontal Displacement 
Actual Horizontal Displacement 
20 



30 



40 



50 



60 



 On one graph plot both the theoretical and the actual range versus
the angle of projection, drawing a smooth curve through each series of
points.
STEP 4 Projected from a Cliff: Measuring Range
 For the chart below you will shoot the JienTze from a ledge or table
that is at least 80 cm high. Run two or three trials for each angle and
record the actual height and range in the chart. [Keep height same throughout]
Angle 
Net Vertical Displacement 
Theoretical Horizontal Displacement 
Actual Horizontal Displacment 
20 



30 



40 



50 



60 



STEP 5 Projected from a Cliff:Calculating Range
 It's too hard to calculate the range in this case, so what we are going
to do is to make a table of height vs. time for each angle, and see at
what time the projectile hits the ground. Then find the x value
at that time.
 On one graph plot both the theoretical and the actual range versus
the angle of projection, fitting a smooth curve (parabola) through each
series of points.
 From the graph, determine the angle of projection for the maximum range
and record the below. Compare with the theoretical prediction of tan q
=
RANGE:
From Actual Graph_________ From Theory Graph _________
From Formulas ______
The essential fact is that all the pictures
which science now draws of nature . . .
are mathematical pictures.
Sir James Jeans
ANALYSIS / CONCLUSIONS
Compare the methods for accuracy and precision. To do this you will
need to compare results with several other students. Determine which method
is consistently accurate. Explain why this method is both accurate and
precise. Why is the theoretical angle for maximum range different from
your actual angle? Why is the smaller angle usually more accurate than
the larger one? Do a vector analysis for one of the methods utilized in
this experimental activity.