Alg1 Lesson 3.11: Gravity and Free-Fall Investigations

Lesson 3.11: Gravity and
Free-Fall Investigations

Obj: 6C, 8B: I can find characteristics of a
quadratic model in context.

EQ: How do I find the maximum height and when
an object hits the ground?

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Roles:
Facilitator
Scribe
Resourcer
Includer

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools
to communicate your mathematics, reasons,
and connections.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may
arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

Which role are you doing?

• Facilitator

• Scribe

• Resourcer

• Includer

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Graphing the Height

of a Thrown Object

Throw a Ball Upward

Jenny throws a ball straight upward as high as she can.
Her friend Marie times her throw and discovers that the
ball was in the air for 3 seconds before it landed on the
ground. Jenny is 5 feet tall, and this was the ball’s
height above the ground at the moment when she
released it. Sketch a graph of the ball’s height as a
function of time.

Drag and Drop

What was the initial height of the ball when it was released? ​

Placeholder

feet above the ground. How long is the ball in the air? ​

Placeholder

seconds

The contextual domain of this function is

​

Placeholder

≤ t ≤​

Placeholder

Drag these tiles and drop them in the correct blank above

5

3

1.5

40

0

4

Drag and Drop

What kind of mathematical shape do we know that could represent an up-and-down motion? A ​

Placeholder

.

According to this graph, what would be the best estimate of the maximum height of the ball?

​

Placeholder

feet

Drag these tiles and drop them in the correct blank above

parabola

jack-in-the-box

spider

quartic

1.5

40

20

34

38

Using Machines to Throw

Jenny and Marie decide to use a pitching machine to
shoot a ball straight upward and time how long it
takes for the ball to come back down. The pitching
machine releases the ball at 5 feet in the air, the
same height that the ball left Jenny’s hand. This time,
it takes 6 seconds for the ball to hit the ground.
Sketch a graph of the ball’s height as a function of
time.

Multiple Choice

Which of the following would most likely be the maximum height of this scenario?

• 40 ft

• 80 ft

• 150 ft

• 260 ft

Part 2: Writing an Equation for
the Height of a Thrown Object

Why a Quadratic Function would be an appropriate model:

● The ball goes up and comes back down
● There is a maximum height
● The graph appears to have symmetry

Quadratic
Forms for
different
situations

Position Formula

h(t) = (acceleration due to gravity)t² +
(initial velocity)t + (initial height)

h(t) = -16t² + v₀t +h₀

-16 feet per second squared, t seconds,
v₀ feet per second, h₀ feet

Formulate Quadratic Equations

0 = -16t² + v₀t + 5

Solve for v₀ for each scenario.

Scenario 1: The ball was in the air for 3 seconds
before it landed on the ground.

Scenario 2: This time, it takes 6 seconds for the ball
to hit the ground.

Multiple Choice

0 = -16t² + v₀t + 5

Solve for v₀ for the scenario: The ball was in the air for 3 seconds
before it landed on the ground.

• 46.33
• 95.17

• 52.19

• 30.25

Fill in the Blank

0 = -16t² + v₀t + 5

Solve for v₀ for the scenario: It takes 6 seconds for the ball
to hit the ground.

.

Drag and Drop

h(t) = -0at² + V₀t +H₀

How would you deal with an object that is simply dropped instead of thrown?

V₀ ​

Placeholder

0
What if an object is thrown downward instead of upward?

V₀ ​

Placeholder

0
What if the object were thrown from ground level?

H₀ ​

Placeholder

0
What if the object were thrown upward from below ground level?

H₀ ​

Placeholder

0

Drag these tiles and drop them in the correct blank above

=

<

>

Part 3: Summary and

Practice

Quadratic Forms for Projectile Problems

Vertex Form: y = a(x - h)² + k if given where and when the
max height is and one other point.

Factored Form: y = a(x - r₁)(x - r₂) if given a starting point and
ending point at the same level (such as two times when on
the ground).

Standard Form: y = ax² + bx + c if given the initial velocity,
initial height, and acceleration due to gravity
(-16ft/s² or -4.9m/s²)

Multiple Choice

Choose the correct answer choice.

• A.

• B.

• C.

• D.

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin
the wheel as a class and spend a minute or so
discussing our answers.