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.  
_____________________________________________________________________

_____________________________________________________________________


b.  Describe change of y.  Be specific.  
_____________________________________________________________________
_____________________________________________________________________

c.  Describe change of Sin (theta).  
_____________________________________________________________________
_____________________________________________________________________

d.  Describe change of Cos (theta).  
_____________________________________________________________________
_____________________________________________________________________

e.  Describe change of Tan (theta).  
_____________________________________________________________________
_____________________________________________________________________

f.  Are the trig functions dependent upon the length of the radius 
(hypotenuse).  Yes/No.  Explain.  
_____________________________________________________________________
_____________________________________________________________________

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? 
_____________________________________________________________________
_____________________________________________________________________
c.  Using your calculator & the sin regression model, graph the 
Chicago 
model.  How well does the model fit the data?  
_____________________________________________________________________
____________________________________________________________________
d.  Use the models to estimate the average annual temperature in 
each city.  
Which term of the models did you use?  Explain.  
_____________________________________________________________________
_____________________________________________________________________
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