MATH 1314 UIdaho Equations of Motion Using Quadratic Functions Probem

MATH 1314 AssessmentEquations of Motion using Quadratic Functions
I)
Introduction:
Equations of motion are used to describe the velocity (speed and direction) as well as
distance travelled by projectiles when they are launched or thrown. The following
equation is used to model this model this movement:
ℎ = −16𝑡𝑡 2 + 𝑣𝑣0 𝑡𝑡 + ℎ0
The variable ℎ represents the height of the object in feet, 𝑡𝑡 represents time in
seconds, ℎ0 represents the initial (starting) height in feet and 𝑣𝑣0 which represents
initial velocity (initial speed) measured in feet/second.
When using this equation we work with the assumption that the object is in “free
fall”, which means it is moving under the sole influence of gravity with no other
external forces influencing its movement. In other words we ignore the effects such
as wind current and friction due to movement (this is not exactly real world, but it
does provide us with a good starting point for predicting the movement of the object).
II) Instructions:
The following steps should be observed to complete this project successfully.
1. Solve the problem listed under “Assessment problem” using the equation and
ideas presented in the “Introduction” section of this document.
2. Write your solution in steps being as detailed as possible. Make sure to clearly
label all of your main steps and show all of the relevant work required to
complete the step.
3. Type the problem statement (purpose of the problem and what is our goal)
together with your solution
4. Include a well labeled and clear graph(s) that help you solve the problem
i)
Draw your graph neatly using a pencil and colored pencils to clearly and
precisely indicate the points and areas of interest, take a picture and
include it in your submission
ii)
Or generate the graph using a computer software of your choice
available on the web, then paste it into the assessment. Be sure to
indicate any points and areas that are important to note.
5. Type a cover sheet using the following format:
MATH 1314 College Algebra Assessment
Equations of Motion using Quadratic Functions
Your Full Name
Odessa College
Your Project’s Due Date
6. You should combine your cover sheet, problem statement, and solution
(including the graph) into a single document, and save it as a pdf file.
7. Submit your finished pdf file through Blackboard. (See “Turning in Your
Project” section below.)
III) Grading
Your grade for this project will be determined based on accuracy,
exposition, and thorough explanation of your work on each of the following
items:
Checklist Components
Points
Problem statement and correct
25
results for the problem
Solving the problem as instructed
65
and showing all of the necessary
work for each part of the question
Aesthetics and presentation quality
10
of the document
Total
100
IV) Turning in your solution
Project must be submitted through Blackboard as follows:
1) Visit your MATH 1314 Blackboard course.
2) Click on “Coursework.”
3) Click on the “MATH 1314 Assessment” folder.
4) Click on “Browse My Computer.”
5) Upload the pdf file of your Project.
6) Click Submit.
V) Assessment problem
A ball is launched upward at 48 feet/second from a platform that is 100 feet
high. Find the maximum height the ball reaches and how long it will take to
get there.
a) Substitute the appropriate values to create an equation of motion for this
problem, using the general equation for motion provided in the
“Introduction section” of this document.
b) Find the vertex of the parabola that the ball will trace. What does this
point represent in the path of motion?
c) Find the x and y intercept of this parabola of motion (the equation you
found above). Round your answers to the nearest hundredth value.
d) Provide the domain and range of this equation. What do these values
represent in our model?
e) Create a graph that accurately represents this motion
f) Find the height that the ball has reached at the following time values:
i)
𝑡𝑡 = 0.7 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
ii)
𝑡𝑡 = 1.0 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
iii)
𝑡𝑡 = 1.2 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
g) Find the height of the ball using the graph and your equation of motion
when 𝑡𝑡 = 1.0 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠. Are these values exactly the same or are they
different? Explain why there may be a discrepancy in the two values.
h) Do the values that you calculated seem reasonable for a ball free falling
through the air? Explain using general logic and expectations.