Ohio State University Mathematics Questionnaire

Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 13.D
1)
Consider a situation in which the coefficient of friction is 𝑓 and the roadway grade
is 𝐺. Let 𝑉0 be in km/h. Which of the following expressions represents the simplified
form of the formula using these values? There may be more than one correct
answer.
a)
b)
𝑉2
0
𝑑 = 2(32.2𝑓𝑡/𝑠𝑒𝑐
2 )(𝑓+𝐺) 𝑓𝑡
𝑑=
c)
𝑑=
d)
𝑑=
(𝑉0
(𝑉0
𝑘𝑚 2 1ℎ𝑟 2 1 𝑚𝑖𝑛 2 1000𝑚 2 3.28ft 2
) (
) (
) (
) (
)
ℎ𝑟
60 𝑠𝑒𝑐
60 𝑠𝑒𝑐
1𝑘𝑚
1𝑚
32.3𝑓𝑡
2(
)(𝑓+𝐺)
𝑠𝑒𝑐2
𝑘𝑚 2 1000𝑚 2 3.28ft 2
) (
) (
)
ℎ𝑟
1𝑘𝑚
1𝑚
9.8𝑚
2( 2 )(𝑓+𝐺)
𝑠𝑒𝑐
0.01289𝑉02
𝑓+𝐺
𝑓𝑡
Questions 2 and 3: A car is traveling 80 km/h on a road with 5% grade.
2)
Plug in the values and perform the possible calculations to write the simplified form
of the formula for the braking distance in meters in this situation.
3)
Complete the table of values for 𝑓 and 𝑑 (in m). Use the values of 𝑓 given in the
table. Round to the nearest tenth of a meter.
𝒇
𝒅 (in m)
0.30
0.50
0.70
0.90
Questions 4–6: A simple pendulum consists of an object attached to a string of length 𝐿
and hangs in a vertical position. The period of the pendulum is the time it takes to make
one full back-and-forth swing. The formula to find the period for the motion of the
pendulum is given by
𝑇 = 2𝜋√
𝐿
𝑔
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
where
•
𝑇 is the period.
•
𝐿 is the length of the string in feet or meters.
•
𝑔 is the acceleration due to gravity (≈ 32.2𝑓𝑡/𝑠 2 or ≈ 9.8 𝑚/𝑠 2 ).
•
𝜋 is a constant ≈ 3.14159.
4)
Find the unit of the period.
5)
Complete the table of values for 𝑇 and 𝐿. Use the values of 𝐿 given in the table.
Round to one decimal place.
𝑳(feet)
𝑻(seconds)
1
4
9
25
6)
If you quadruple the length of the pendulum, how does that affect the period? What
if you make the length of the pendulum nine times longer or twenty-five times
longer?
The following problem should be printed out, completed, and placed in your
binder.
Mathematical formulas
7)
Search the web for mathematical formulas in physics or chemistry. Record two
formulas (e.g., Gas Law) that you have not yet used in this course. Tell what each
variable represents and give an occupation that might use this formula.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 13.C
Questions 1–4: In In-Class Activity 13.C, you investigated the relationship between
velocity and braking distance. You will now investigate the relationship between the
coefficient of friction and the braking distance.
Recall that the formula for the braking distance of a car is
𝑑=
1)
𝑉02
2𝑔(𝑓 + 𝐺)
Complete the table below by defining each variable, including its units if applicable.
State if there are no units.
Variable
Description
Units
𝑉0
𝑑
𝐺
𝑓
𝑔
2)
Which of the variables listed in Question 1 always represents a constant?
3)
To investigate the relationship between the coefficient of friction and the braking
distance, you need to hold the other variables fixed. Let 𝐺 = 0.02. Which of the
following is a correct interpretation of the value 𝐺 = 0.02?
4)
a)
The grade of a road is 0.02%, which is a vertical increase of 0.02 feet for
every 1 foot of horizontal increase.
b)
The grade of a road is 0.02%, which is a vertical increase of 0.02 feet for
every 100 feet of horizontal increase.
c)
The grade of a road is 2%, which is a vertical increase of 2 feet for every 1
foot of horizontal increase.
d)
The grade of a road is 2%, which is a vertical increase of 2 feet for every 100
feet of horizontal increase.
Let 𝑉0 = 72 mph and 𝐺 = 0.02. Which of the following expressions represents
the simplified form of the formula using these values?
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
11,151.36
a)
𝑑 = (64.4𝑓+0.02) 𝑓𝑡
b)
𝑑=
c)
𝑑 = (64.4𝑓+1.288) 𝑓𝑡
11,151.36
64.4𝑓
+ 8,657.89𝑓𝑡
11,151.36
Questions 5–7: A car is traveling 60 mph on a road with 4% grade. The simplified form
of the formula in this situation would be:
𝑑=
7,744
𝑓𝑡
64.4𝑓 + 2.576
𝒇
𝒅 (feet)
0.30
0.50
0.70
0.90
5)
Complete the table of values for 𝑓 and 𝑑 (in feet). Use the values of 𝑓 given in the
table. Round to the nearest hundredth of a foot.
6)
The four values of 𝑓 in the table correspond to the coefficient of friction for four
road conditions: an icy road, a very good road with great tires, a medium-quality
road with worn tires, and a wet road with fair tires. Match the coefficients of friction
to the appropriate conditions by looking at the braking distance required. You are
welcome to search the internet to get a better idea of what it is like to drive in these
conditions, if necessary.
o Icy road, 𝑓 =
o Very good road with great tires, 𝑓 =
o Medium-quality road with fair tires, 𝑓 =
o Wet road with fair tires, 𝑓 = Type equation here.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
7)
The coefficient of friction (𝑓) is increasing at a constant rate, since each value is
0.2 more than the previous value. How is 𝑑 changing as 𝑓 increases at a constant
rate?
8)
a)
The stopping distance is decreasing.
b)
The stopping distance is constant.
c)
The stopping distance is increasing.
A cyclist was traveling along Highway 7 in British Columbia
and saw the sign to the right.1
Part A: What is the maximum speed in feet per second?
Round to the nearest tenth of a foot per second.
Part B: If 𝑓 = 0.8, find the braking distance in miles for the a
driver on this road. Round to the nearest foot.
Credit: J. Werner
Question 9: In Lesson 7, you used a formula that was written as steps in a form to
calculate self-employment taxes for different people. Formulas are often written in this
way. One example is the Expected Family Contribution (EFC) Formula, which is used to
determine if a college student is eligible for financial aid. The EFC has many different
sections that each use different calculations. One section of the 2010–11 form is shown
below.
Student’s Contribution from Assets
45
Cash, savings, and checking
46
Net worth of investments
If negative, enter zero
+
47
Net worth of business and/or investment farm
+
48
Net worth (sum of lines 45 through 47)
49
Assessment rate
×
50
Student’s contribution from assets
=
1
Werner, J. (2009). Silver Circle Bicycle diary. Retrieved September 17, 2020, from
jeffwerner.ca/blog/2009/08/silver_circle_bicycle_diary.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
0.20
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
9)
Calculate the student’s contribution from assets given the following information.
Round to the nearest dollar.
Cash: $500
Investments: net loss of $2,000
Savings: $3,240
Business: $0
Checking: $732
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin