Representing quadratic Models
Students will learn the effect that gravity has on a projectile, understand how projectile travel creates a parabolic curve, and understand the equation for projectile travel.
Essential Question:
If given the height and the initial velocity of an object, how can one predict the height of a projectile?
I often take for granted the physics and math involved in every-day life. This lesson brings to life the concept of projectile travel. In the movie October Sky, Jake and his friends experiment with launching rockets. After many failed attempts, they successfully launch a rocket and have it land safely back on earth. Their success is short lived as they are accused of starting a fire in a coal mine 3 miles from their launching pad. Let us have a conversation of what it took to get the rocket in the sky.
For the full lesson please visit AIMS non-profit organization that put this lesson together.
For the full lesson please visit AIMS non-profit organization that put this lesson together.
Warm-Up:
Discuss your knowledge of parabolas. At this point, we have already gone through most of the vocabulary that deals with quadratics.
What is a parabola?
What is the Axis of Symmetry (AoS)?
What is happening to the function at the Vertex?
What do the Zeros of the function represent?
What is the relationship between rockets and parabolas?
What is a parabola?
What is the Axis of Symmetry (AoS)?
What is happening to the function at the Vertex?
What do the Zeros of the function represent?
- Identify the Axis of Symmetry (AoS)
- Identify the Vertex
- Identify the Zeroes (or Roots) of the function
What is the relationship between rockets and parabolas?
The Setup
Watch this video. After many failed attempts the rocket boys eventually get the rocket to successfully launch and land safely. Caution: There is a bad word at 39 seconds.
The journey
The worksheets that go along with this activity can be found in the book Movie Math Mania or use the link in the intro to just purchase lesson. The table and graph allow for students to track the coordinates of the rocket through its path. Here is what their graph and data will look like.
For paperless interaction use Desmos to plot the points. Initially, you will realize that the path is modeled by a
linear relationship, but that cannot be right. Have a conversation about why
this cannot be right. Can this little rocket go into space and beyond? The rocket
does not travel into outer space and continue traveling endlessly- it came back
to earth. Why?
Model the data from the movie and graph those new data points. The new data should reveal a new path that does include the effects of gravity. This graph can be used to discuss the difference between predicted height and actual height. That difference turns out to be the gravitational constant that is present in the real world and Hollywood.
Model the data from the movie and graph those new data points. The new data should reveal a new path that does include the effects of gravity. This graph can be used to discuss the difference between predicted height and actual height. That difference turns out to be the gravitational constant that is present in the real world and Hollywood.
Get Techy With it
By using Desmos calculator, each student can model the relationship with both sets of data and come to a conclusion of what the right equation should be that models a projectile and can identify the parts.
Resolution
This is the last clip as Homer proves why he and his friends did not start the fire. In his explanation, he arrives at some very familiar numbers that you should now recognize.
Extension
Have students create their own rockets to represent the quadratic function based on information gathered from the lesson and Jake's explanation.