Practicing Projectile Path Math

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Objective

Given its initial conditions, students predict the horizontal displacement of a projectile .

Big Idea

The x and y velocity components of a projectile can be analyzed independently of one another.

Context

Students apply the kinematic equations to the projectile motion velocity components. This is a challenge as we have to rename many of  the variables as we apply the constant velocity formula to the x-components and the constant acceleration formulas to the y-components.

This lesson builds off of the previous lesson which introduces projectile motion. Students apply what they know about the velocity vector components for a projectile to solve a variety of problems. This is related to the NGSS HS-PS2-1, where students 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. Students also develop a mathematical model of projectile motion which applies CCSS Math Practice 4: model with mathematics and NGSS Science Practice 2: develop and use models.


 

Do now: projectile graph matching

5 minutes

At the beginning of class, I display the projectile motion graphs matching sheet with my document camera, with the answers covered up. Students draw this situation in their notebooks and then match the graphs to the descriptors. This is a review of what students learned in the previous lesson about a projectile's velocity, velocity components and acceleration in the horizontal and vertical directions. This also applies multiple representations of motion via the graphs which is good for student learning.

After 5 minutes, I call on students to supply their answers and the reason why they choose that answer.  I like to have students supply the answers as much as possible as it reveals to me their thinking and it is good for students to see their peers understanding. After we have reviewed the students answers, I reveal the solutions printed on the sheet by moving the paper.

Lecture on solving projectile motion problems

15 minutes

Direct instruction is a great way to provide information quickly. Lecture is also a good way to model effective methods of problem solving. This Projectile sample problems Power Point is presented to the students at the beginning of class. I review the projectile motion equations on the opening slide by calling on random students to explain the meaning of each of the variables.

Then I present the students with a sample problem and proceed to solve the problem sharing my thought process along the way. Students are to write all of this information in their notebooks, along with important comments that I make. For example, I will say what I know about the projectile at the maximum height, "The vertical velocity vector is zero at the peak of the motion. This is an important factor for solving the maximum height so make sure you write that down!" or "Since the x-component of the velocity is constant at all points, all I need is the time to figure out the horrizontal displacement. Write that down next to the equation x=vxt!"

As I lecture, I watch students to ensure they take notes. I'll look at their notebooks as I walk around to see what kind of detail they record. If I notice a student's notes are lacking proper detail, I bend down and whisper to them to provide more detail or I call them over at the end of class to discuss their note taking.

 

Students solve projectile motion problems

30 minutes

While direct instruction is a quick way to provide students information, it is essential that they engage and practice these problems on their own so that they can develop the skills needed to make predictions about projectile motion. This is time for them to practice the speed and accuracy in projectile motion as I hand out the projectile practice worksheet. Students have the remainder of the class period to work on these problems. If they don't finish them in class, they are expected to complete them for homework. 

While students are working on these problems, I am circulating the class with the Projectile practice solutions in hand. I do not let students see the solutions, but I use them to check their work and help them where needed. As the class period comes to an end, I inform students who have not finished the worksheet that they can finish it for homework, I collect those that finished.

I tell the whole class to be ready for an exciting day tomorrow, as they will be "put to the test!"  I reveal the projectile launcher and tell them that they will put all they have learned today into action as they have to predict where the projectile will land. And they only get ONE SHOT!