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Project #9. Due NLT 12 Jan. Page 693. Do all parts.
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Project #3. Due NLT 16 Dec. Page 279. Do all parts. For question
1b on the bottom, recommend you using the following computer program
to speed up the process.
Program Name - INT
Input P
Input R
Input T
Lbl A
P*R/100*(100-T)/100+P -> P
Disp P
Pause
Goto A
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Project #2. Finding Points of Intersection. Page 213. Upper Half
problems 1 and 2. Bottom Half problems 1 thru 4. Due on 18 Nov.
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Project #6. Separate Handout. Due 31 Oct.
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AMPLIFYING INSTRUCTIONS
PROJECT #5, PROJECTILE MOTION
(PARAMETRIC EQUATIONS AND TRIG)
Page 425. Round all answers to two decimals when appropriate.
Part I. Initial part contains four questions as outlined in the
white portion of the page. This serves as an introduction to
Parametric Equations. Instructions provided are very specific.
Follow the instructions carefully. Answers will be approximations.
Question d is referring to the physical range of the projectile vice
the function range. In other words, the range being referred to is
how far does the projectile actually travel.
Part II. These are the five questions listed in the shaded portion
of the page.
� Question 1. You are to accomplish two things here. First,
you should be able to algebraically solve for t. Hint - factor and
solve. You will have two solutions but one of them will be trivial,
t=0. Use your other value of t to solve the second part of this
question. Evaluate x(t) at this value. Compare your answers here
to what you found in Part I. Discuss any discovery.
� Question 2. Switch back to the functional and degree mode
in your calculator. You should be able to find the maximum height
of the projectile from the graph. You should also be able to find
the value of t when the projectile returns to the ground (returns to
the x-axis). Use this found value of t and the x(t) formula given
in the book to find the maximum physical range. What is the
discovery here? Specifically, what happens when you increase the
initial velocity and increase the angle of elevation from 20 to 30
degrees?
� Question 3. In this question you are fixing the initial
velocity at 60 feet per second, and experimenting with changes in
elevation. One way to analyze this question is to work this in two
steps. Step 1, set y(t) equal to zero and find the non-trivial
values of t for the different angle measurements. Write down those
values. Then, take those values of t which represent the time when
the projectile returns to the ground, and evaluate x(t). These
answers will represent the maximum physical range of the projectile
for each of the different angles of elevation. You should make a
discovery here. At what angle do you think the physical range is
maximized?
� Question 4. You can use your Algebra II skills to answer
this question.
� Question 5. Follow the directions develop (show) how to
arrive at the final equation of y in terms of angle theta, x, and
the
initial velocity. As stated, use that equation to find the angle of
elevation that maximizes the range given that the maximum range at
an initial velocity of 80 feet per second is 200 feet. Linchpin �
what is that value of y when the range is maximized (returns to the
ground). Once you decide this value of y, substitute it in for y,
200 in for x, and 80 in for v and solve for the angle theta. You
will need your skills from Lesson 5.3 in order to find this answer.
Once you have your answer, go back and look at what your last answer
from Part II, Question 3. There should be a direct connection
here. If successful, you should be able to firm up your answer to
the question, at what angle is the physical range maximized.
Due 17 Oct. Late Fee � 10 points per day.
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Project #4 (20 points per problem. Show work on separate paper.)
Lesson 4.1
#92, Page 293
a. Find number of degrees of rotation. _____________
b. Find number of radians of rotation if it takes 3 sec to lift the
item 1
foot. _______________
c. Find linear speed. _____________
d. Find angular speed. ____________
Lesson 4.1
#96, page 294
a. Find angular speed in radians per minute. ________
b. Find angular speed in radians per second. ________
c. Find linear speed in feet per minute. __________
d. Find linear speed in feet per second. __________
Lesson 4.3
#70, page 312
a. Find arc length from (56,0) to (x1, y1). ________
b. Find arc length from (x1, y1) to (x2, y2). _______
c. Find arc length from (x2,y2) to (0,56). _______
d. Find point (x1, y1) in radical form. _______
e. Find point (x2, y2) in radical form. _______
Lesson 4.4
#112, page 322
a. Describe change of x. Be specific.
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_____________________________________________________________________
b. Describe change of y. Be specific.
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c. Describe change of Sin (theta).
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d. Describe change of Cos (theta).
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e. Describe change of Tan (theta).
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f. Are the trig functions dependent upon the length of the radius
(hypotenuse). Yes/No. Explain.
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_____________________________________________________________________
Lesson 4.5
#84, pages 332-333. Parts b thru f inclusive.
b. Using your calculator & the sin regression model, graph the
Honolulu
model. How well does the model fit the data?
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_____________________________________________________________________
c. Using your calculator & the sin regression model, graph the
Chicago
model. How well does the model fit the data?
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d. Use the models to estimate the average annual temperature in
each city.
Which term of the models did you use? Explain.
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_____________________________________________________________________
e. What are the periods of the two models? Are they what you
expected?
Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
f. Which city has the greater variability in temperature throughout
the
year? Which factor of the models determines this variability?
Explain.
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Due Date - 2 Oct 08
Late Fee (10 points per day)
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Project #1, Page 133. All
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