Projectile Trajectory CEPA
Purpose: To model landing the human cannon ball in the net while keeping the
velocity of the cannon and the distance constant.
Description: To better engage the crowd, Emmanual Zacchini of Ringling Brothers
and Barnum Bailey circus proposed launching himself at a low angle and then, to
dazzle the crowd, a greater angle as Mr. Zacchini launches over the flying trapeze.
While liking the act, the ring master was concerned about the liability and asked
Mr. Zacchini to model his act first and prove that the calculations would work
reliably.
Students will measure the time and be given the distance to calculate the velocity
of the projectile launcher. They will be given the smaller of two angles of launch.
They must calculate the distance away that the net must be placed to catch scale
shaped Mr. Zachinni. Next a second launch at the complimentary angle will be
completed to dazzle the crowd. Students must prove mathematically what the
correct distance should be for the nets placement and then prove it with three
actual launches. Students will write up their research in a manner that is clear for
others to understand and they will write a conclusion that defends their data.
Next Gen Science Standards
HS-PS2-1
HS-PS2-4
Analyze data to support the claim that Newton’s second law of
motion describes the mathematical relationship among the net
force on a macroscopic object, its mass, and its acceleration
Use mathematical representations of Newton’s Law of Gravitation
and Coulomb’s Law to describe and predict the gravitational forces
between objects.
From the Massachusetts Frsmeworks
1. Motion and Forces
Central Concept: Newton’s laws of motion and gravitation describe and predict the
motion of most objects.
1.1 Compare and contrast vector quantities (e.g., displacement, velocity, acceleration
force, linear momentum) and scalar quantities (e.g., distance, speed, energy, mass,
work).
1.2 Distinguish between displacement, distance, velocity, speed, and acceleration.
Solve problems
involving displacement, distance, velocity, speed, and constant acceleration.
1.3 Create and interpret graphs of 1-dimensional motion, such as position vs. time,
distance vs. time, speed vs. time, velocity vs. time, and acceleration vs. time where
acceleration is constant.
1.4 Interpret and apply Newton’s three laws of motion.
1.5 Use a free-body force diagram to show forces acting on a system consisting of a
pair of interacting objects. For a diagram with only co-linear forces, determine the net
force acting on a system and between the objects.
1.6 Distinguish qualitatively between static and kietic friction, and describe their
effects on the motion of objects.
1.7 Describe Newton’s law of universal gravitation in terms of the attraction between
two objects, their masses, and the distance between them.
Materials Provided
Launcher, stand, 2 timer gates, 1 timer, net, ball to symbolize Mr. Zacchini,
calculator with trig functions
Accommodations/ Modifications
As identified in either the IEP or 504 plan for a given student. Typical
accommodations to include but not limited to; definitions for vocabulary, a
formula sheet, and extra time. However students will have no more than 1 extra
time period to complete the data collection and calculation.
Overview of Task
The ringmaster has asked you Mr. Zacchini to liven up your performance. While a
low angle trajectory is interesting for the audience to watch, The ringmaster has
suggested you being shot over the flying trapeze act while it is in progress. Since
setup time for the net takes so long, the ringmaster doesn’t want you to move it
between the two different launches. On a scale model you will need to do the
calculations to prove where the net should be located with a 20 degree and
complimentary angle trajectory and after calculating the velocity you will need to
find the apex of the path. Accuracy is critical as Mr. Zacchini’s life depends upon
you.
Your task requires you to correctly calculate and measure time, distance, velocity,
apex height and horizontal distance, then record the data in an organized manner
for others to understand. Calculations should be completed to three significant
figures. Do not round off.
Record time, velocity, horizontal distance, and the apex both calculated and
measured where possible.
Prove to the trapeze artists that you will safely sail over their heads knowing the
maximum height the trapeze artists achieve is 1.5 meters.
Product to Hand In
1. Detailed procedure of how you accomplished this exercise.
2. All calculations completes using KUESA
3. Calculate the percent of error between the measured and calculated results
with possible areas identified that could be the cause of the error.
4. Write a conclusion that is defended by your data
You have three class periods to complete your product for this Projectile Lab.
Evaluation Rubric
Category
4
3
2
1
Procedure
Detailed
Detailed procedure
identifying the steps
needed in the proper
order to accomplish
this task. Steps are
numbered. The
correct vocabulary is
used
Calculations
Calculations were
performed correctly
using KUESA and laid
out in the report in a
clear logical linear
manner. Answers
are accurate to three
significant figures.
Procedure is either
not detailed or a
step is missing.
Steps might not be
numbered.
Incorrect
vocabulary is used
at least twice.
Calculations were
done correctly but
KUESA was not
used or
calculations were
not laid out in a
logical order.
Procedure will not
lead to success.
Several steps are
either missing or
incorrect.
Vocabulary is
either missing or
used incorrectly
Calculations were
not done correctly
and the sequence
followed by the
student is unclear.
Measurement
Measurements were
performed correctly
and laid out in the
report in a clear
logical linear
manner.
Measurements are
reported to three
significant figures.
Measurements
were performed
correctly were not
laid out in a clear
logical linear
manner. At least
two
measurements
were not reported
to three significant
figures.
Procedure is
missing several
steps or the steps
are unclear.
Incorrect
vocabulary is used.
Steps might not be
numbered.
Calculations were
not done correctly
but are laid out in
a clear manner
allowing for the
reader to
determine where
the lab technician
made their error.
KUESA was
attempted.
Measurements
were not done
correctly but are
laid out in a clear
manner allowing
for the reader to
determine where
the lab technician
made their error.
Measurements
were not reported
to three significant
figures.
Conclusion
Conclusion includes
what was learned
about calculating
and measuring the
Apex Height and
Horizontal Projectile
Distance. It points to
a percent of error of
less than 10%. The
proper vocabulary is
used in the
conclusion. Sources
for the discrepancies
between calculated
are identified.
Conclusion includes
what was learned
about calculating
and measuring the
Apex Height and
Horizontal Projectile
Distance. It points to
a percent of error of
less than 13%. The
proper vocabulary is
mostly used in the
conclusion. Sources
for the discrepancies
between calculated
are identified.
Conclusion includes
what was learned
about calculating
and measuring the
Apex Height and
Horizontal Projectile
Distance. It points to
a percent of error of
less than 18%. The
proper vocabulary is
missing. Sources for
the discrepancies
between calculated
are not identified.
Conclusion does not
include what was
learned about
calculating and
measuring the Apex
Height and
Horizontal Projectile
Distance. Percent of
error is either
missing or > 18%.
The proper
vocabulary is
missing. Sources for
the discrepancies
between calculated
are not identified.
Measurements
were not done
correctly and the
sequence followed
by the student is
unclear.
Measurements
were not reported
to three significant
figures.
Student
Score
Teacher
Score
Teacher Notes
This is an end of unit summative assessment for projectile motion. Students
should be able to complete this with little difficulty as they have read about
projectile motion, had several quizzes on projectile motion, taken a written exam,
and completed three labs on the subject. The CEPA should be introduced shortly
after the start of the unit so students will become familiar with the terminology,
and equipment they will need to complete this assessment.
Vocabulary:
 Sine Function- The ratio of the side opposite the angle described to the
Hypotenuse
 Distance- As measured in meters
 Time- as measured in seconds
 Velocity- As measured in meters per second
 Acceleration- This is gravitational acceleration on earth at a rate of 9.8
meters/second2
 Trajectory- The path the projectile will travel
 Projectile- an object that moves through air or space acted on only by
gravity (in this case earth’s gravity) air resistance will be ignored in this
example.
 Apex- the maximum height achieved.
 Theta – The term used in place of an unknown acute angle.