Projectile Motion                     

 

LESSON PLAN #                                                 

           

Technology Lesson?   No

                               

Name(s): Albert Alvarado

 

Title of lesson: Introduction to Parametric Equations and Applications of the Kinematics Equation

 

Length of lesson: 150 minutes

 

Description of the class:

                     Name of course: Pre-Calculus

                     Grade level: 11th – 12th grade

                     Honors or regular: Regular or Honors

 

Source of the lesson:

Source:http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L6d.html

 

TEKS

 

111.35 Pre-Calculus

 

(P.3)  The student uses functions and their properties, tools and technology, to model and solve meaningful problems.

            (A)  investigate properties of trigonometric and polynomial functions;

 

            (E)  solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

 

(P.6)  The student uses vectors to model physical situations.

            (A)  use the concept of vectors to model situations defined by magnitude and direction; and

 

            (B)  analyze and solve vector problems generated by real-life situations.

 

I.       Overview

Students will be able to work with the parametric system and will have been introduced to the kinematics equations that govern motion.

 

II.  Performance or learner outcomes

·         Students will be able to go from the parametric system to the coordinate system.

·         Students will be able to model situations using the parametric system.

·         Students will learn the kinematics equations and real life problems using the kinematics equations.

 

II.    Resources, materials and supplies needed

Overhead

Transparencies

At least one computer to pull up applet

 

IV. Supplementary materials, handouts. (Also address any safety issues

      Concerning equipment used)

Introduction to Parametric Equations Worksheet

Modeling with Parametric Equations Worksheet

Kinematics Equation and Real Life Problems

 

 

Five-E Organization

Teacher Does                    Probing Questions                     Student Does     

Engage:

Anchor Video

 

Trig Refresh

Give students a handout on trig and discuss some of the trig concepts that they may have forgotten.

 

Go over vectors then discuss how they will apply to Parametric Equations.

 

Discuss the Vector equation of a line. (x,y) = (a,b) + tv

 

Students will be given the worksheet Introduction to Parametric Equations and discuss how parametric equations are derived from the Vector equation.

 

 

In the vector equation what does the v stand for?

Can v be written in a different form?

How does this differ from equations that you’ll have seen previously?

 

 

 

Student should stay active in class and think about how vectors from the previous lesson tie into the vector equation.

 

Students should complete the worksheet Introduction to Parametric Equations.

 

 

 

 

 

 

 

 

 

                                                   

Explore:

The students will explore projectile motion on the website.

www.ac.wwu.edu/~vawter/PhysicsNet/QTMovies/Vectors/ProjectileMotMov.html

 

This could be done as a class or each student could do this on their own depending on how much computers are available.

 

During this day the students will work on modeling parametric situations using the equations

 

x = (vo cos Ө) t 

y = -16t2 + (vo sin Ө) t + so

 

 

 

 

 If there are several computers available with internet you can lead students to the applet and discuss how projectile motion is governed. Students will follow along.

 

If only one computer is available then you can just show the students the applet in the front of the room through a projector.

 

 

 

 

 

 

 

If there are several computers available with internet you can lead students to the applet and discuss how projectile motion is governed. Students will follow along.

 

If only one computer is available then you can just show the students the applet in the front of the room through a projector.

 

 

 

    

Explain:

Explain the worksheet Modeling Parametric Equations. Work through a few problems then have students finish the worksheet.

 

Approx. Time 50 mins

 

What situation can you model that would involve the variable of time?

 

 

 

 

Students should follow along and take notes on problems that are worked in class. Then students should work on the worksheet Modeling Parametric Equations

                                               

Extend / Elaborate

 

During this lesson students will get into groups and extend their knowledge of parametric equations to the kinematics equation. These will be real life extensions to the kinematics equations.

 

Ask students from yesterdays lesson how they think projectile motion can be modeled? This should be review for them.

 

Students will break into groups of 2 or 3 and begin to work on solving problems using the kinematics equations.

   

  Evaluate:

Students will take a quiz on the parametric equations, modeling motion using parametric equations, and Kinematics Equations.

 

Approx. 50

 

 

Student will complete the quiz and turn it in to be graded.