Projectile Motion

ABSTRACT-

            The purpose of this unit is for students to gain valuable knowledge of vectors, parametric equations, the kinematics equations, and applications of statistics and software to map out functions of projectile motion. Interest in physics and mathematics is declining and the unit that we propose is an effective method to alleviate this issue at a local level by teaching students mathematic concepts that are applicable to projectile motion.

RATIONALE-

            The rationale of the unit of projectile motion is for students to be introduced to real life applications of mathematics in the physical world that would allow students excellent preparation for physics and mathematics courses at the collegiate level. This lesson would greatly benefit communities with students of lower economic status because this would allow those students an opportunity to learn projectile motion in a more interactive manner than the typical classroom setting. By the end of the unit students will have grasped the concepts parametric equations, vectors, kinematics equations, an introduction to statistical methods, data analysis, and an introduction to the use of logger pro software and video editing (to be explained in great detail in the description) where students will be able to map the motion of their projectile over time. This is a great way for students to experience the power of mathematical functions to map out real world situations.

            It is our hope that the lessons learned in this unit will positively impact students and will give them knowledge in mathematics and physics in a way they haven’t experienced before at the high school level. This is the kind of unit that could significantly influence a student to get into a field relating to mathematics or physics such as mechanical engineering, statistics, or data analysis.

DESCRIPTION-

            The lesson is based on projectile motion and differs from the normal classroom setting in that students are able to work with real motion and experiment on how the concepts of parametric equations, vectors, and physics tie into real world applications. The lesson will be exciting for students because students will have an opportunity to experiment with these concepts through the use of catapults. Students have experienced projectile motion their entire lives through sports and other mediums but more then likely this will be students’ first experience modeling the motion of a projectile mathematically.

            The students will begin the unit with a brief three day introductory lesson to the properties of vectors including how to scale and add them. During this period they will begin to understand how they can be applied to the real world through word problems. This will be followed by a quiz in which students will test their knowledge on vectors. Similarly students will go through a 3 day lesson on parametric equations with a trigonometry refresh leading into the use of the kinematics equations, or the equations that govern motions of projectiles. This will teach students how to solve problems with parametric equations with and without the use of TI 83 Calculators which will simultaneously increase their abilities in solving equations and using technology of the TI 83 Calculators. Once students are more comfortable with parametric equations they will begin to see its applications through the kinematics equations and then see how these equations govern projectile motion. These concepts will be assessed at the end of the lesson through the students’ second quiz.

            Now the previous 3 day lessons on vectors and parametric equations were necessary for the students to be successful in the 9 day project that will follow. The project will peak student’s interest by allowing them to pick a sport between football, soccer, baseball and volleyball. The objective is to have students map and describe the motion of their respective ball. So prior to beginning this project students will be briefed on how to use the logger pro software that will allow them to map the motion of their projectile. They will also be introduced to scientific and statistical methods of analyzing data that they will apply in their experiment. So over the time period of this lesson groups of students will work together and use cameras to record the motion of their respective projectiles. The video they obtain will be uploaded and analyzed through the use of Logger Pro software. Once the groups have collected their data they will analyze the data using statistical methods then present a conclusion. The groups will then be required to formalize their projects with a Power Point presentation. The presentation will be evaluated by both the students and the teacher through a rubric on presentation, how well they collected their data, how well do they understand their data and conclusion, and if each group member worked equally in the experiment.

            As an extension the final portion of this unit will be a role play for the students where they will have a mission to target an opposing teams’ mascot (or some other target). Different groups will be given different distances in which they need to target. It is each group’s job to calculate and construct a catapult that would hit their target in the classroom or in a large area. As the finale during the second to last class day of this unit students will be able to test their calculations and will be graded on the accuracy of their calculations and whether or not they were able to hit their target. This will be an exciting finale for the students that will reinforce them that the mathematical concepts they covered can be applied to real world physics.

CALENDER-

BUDGET-

5 Digital Cameras - $1145.00

Mini DV Tapes - $14.99 (2)

Logger Pro Software - $159

Apple Computers - $1,299.00

Microsoft Office - $29.99

LCD Projector - $799.99

Meter Sticks - $2.69 each

Measuring Tape – $17.99 each

Tripod - $279.99

Basketball - $16.99

Baseball, gloves, bat - $219.98

Football - $13.98

Soccer ball - $17.76

Volley ball - $29.99

Markers - $8.19

Poster Boards - $3.89

Garden Stake - $29.97

Milk Carton  - Recycled

Scissors - $3.19

Graph paper - $9.99

Rubber bands - $4.43

Pencils - $3.59

Tape - $3.99

Toothpicks - $1.00

Small match box - $.99 (1 per student)

Hole puncher - $9.19

Marble - $1.00

Geometer’s Sketchpad – $39.99

EVALUATION PLAN-

            The main goal of our unit on projectile motion is to allow students an opportunity to learn the concepts of vectors, parametric equations, kinematics equations, and to use software and statistical methods to analyze real world projectile motion. The two three day lessons of vectors and parametric equations will both be evaluated by quizzes. The project on the other will be evaluated during the course of the project and by the quality of work they present for their final presentation. The final presentation of the project is to be evaluated by both the students and teacher through the use of rubrics. To ensure that the students all work together they will each submit a group summary at the completion of their project detailing who did what in the project. To keep students on track I will have each group create a detailed schedule for the 8 days they are to work on the project. During each class period students will be required to fill in a log of what they completed that day and will be given a daily grade depending on how well they kept to there schedule and if they made a day’s worth of progress.  This will prevent students from waiting to the last minute to complete the project which is what tends to happen when students are given class time to complete a project.

            For the extension of this project student groups will be graded on the precision of their calculations and whether they hit their intended target or not. Following this will be one last final assessment with a quiz on projectile motion that will test students on the ideas learned from the projects they have completed.