Copy of PHYS110 Motion in Two-Dimensions Lab - STUDENT VERSION (2)
.docx
keyboard_arrow_up
School
Siena College *
*We aren’t endorsed by this school
Course
110
Subject
Physics
Date
Apr 3, 2024
Type
docx
Pages
9
Uploaded by ec20broo
Siena College - General Physics 110
Motion in Two-
Dimensions Lab
NAME:
Emily Brooks
GROUP MEMBERS: Lisa, AG,
Kamini, Sylvia
Learning Goals
1.
In Section I, you will investigate the horizontal and vertical components of a projectile’s velocity and devise an explanation related to whether or not each component of velocity is dependent on one another.
2.
In Section II, you will design a new qualitative experiment to test the explanation that you devised in Section 1 related to whether or not each component of velocity is dependent on one another.
3.
In Section III, you will quantify the launch speed of a projectile, and use this quantification to predict how far the projectile will travel when launched at a certain angle.
Section I - In this part of the lab, you will investigate the horizontal and vertical components of a projectile’s velocity and devise an explanation related to whether or not each component of velocity is dependent on one another.
Equipment: “Ball and Cart” video In this part of the lab, you will watch a video of a ball being launched when the cart upon which the ball resides is subject to either no horizontal push or different amounts of horizontal push. You will observe and record the patterns you notice for the motion of the ball and cart with respect to different frames of reference (for example: the cart’s motion relative to the table, etc.). You will then come up with an explanation for the direction of the launch that lets the ball land successfully back into the launcher.
Scientific Ability
Missing
Inadequate
Needs Improvement
Adequate
A6
Motion Diagram
No representation is
constructed.
The motion diagram does not show the proper motion: either the lengths of
the arrows (both velocity and velocity
change) are incorrect or missing and/or the spacing of the dots are incorrect.
The motion diagram has the correct spacing of the dots but is missing velocity arrows or velocity change arrows.
The motion diagram contains no errors and it clearly describes the motion of the object.
Dots, velocity arrows, and velocity change arrows are correct.
B5
Is able to describe what is observed without trying to explain, both in words and by means of a picture
of the experimental No description is mentioned.
The description is incomplete. No labeled sketch is present. Or, observations are adjusted to fit expectations.
The description is complete, but mixed up with explanations
or patterns. The sketch is present, but it is difficult to understand.
Clearly describes what happens in the experiments both verbally and with a sketch. Provides other representations when necessary 1
Siena College - General Physics 110
Motion in Two-
Dimensions Lab
setup.
(tables and graphs).
B9
Is able to devise an explanation for an observed pattern
No attempt is made
to explain the observed pattern.
An explanation is vague, not testable,
or contradicts the pattern.
An explanation contradicts previous knowledge
or the reasoning is flawed.
A reasonable explanation is made. It is testable and it explains the observed pattern.
A4
Is able to use representations to
solve problems
No attempt is made to solve the problem.
The problem is solved correctly, but
no representations other than math were used.
The problem is solved correctly, but
there are only two representations: math and words explaining the solution.
The problem is solved correctly with at least three different representations (sketch, physics representation, and math OR sketch, words, and math, OR some other combination).
Watch the video, “Ball and Cart”:
https://www.islephysics.net/pt3/experiment.php?topicid=2&exptid=94
A.
Observe the motion of the ball and the cart, and describe what you observe in simple words.
The ball was launched from the cart moving in one direction. The ball launched
up positively in the Y axis and negative in the x direction. The ball then reached it’s peak high and fell continuing in the negative x direction and negative y direction at the same but opposite angle of travel.
B.
Observe the motion of the cart with respect to the table. Draw a motion diagram representing the motion of the cart. In words, describe the motion of the cart relative to the table.
The cart is moving in a linear line on the table. The cart will continue at a constant speed until an external force will be acted upon it. acceleration=0
--->--->--->--->--->--->--->
∆V =0
C.
Observe the motion of the ball with respect to the cart. (It is helpful if you can step your video frame by frame.) Draw a motion diagram representing the motion of the ball with respect to the cart. In words, describe the motion of the
ball relative to the cart.
2
Siena College - General Physics 110
Motion in Two-
Dimensions Lab
1.
it ascends in the positive vertical direction with a decreasing velocity (velocity vector is upward, acceleration is -9.8m/s^2)
2.
it comes to a halt in mid-air at the peak of its trajectory (velocity is 0, acceleration remains -9.8 m/s^2)
3.
it descends in the negative vertical direction with an increasing velocity (velocity vector is downward, acceleration is -9.8 m/s^2)
D.
Observe the motion of the ball with respect to the table.
What pattern do you see? What can you say about the
motion of the ball and the cart with respect to each other
that is always true? Draw a motion diagram representing
the motion of the ball relative to the table.
The acceleration vector points downward (due to the
constant acceleration of (-9.8m/s^2), the velocity vector
is downward and the force vector also points downward
(since the only force acting on the ball is gravity, which always pulls downward).
E.
How is the motion diagram you constructed in part d. related to and consistent
with the motion diagrams in parts b. and c.? Is there a relationship? What is it?
Work with your group members to come up with an explanation for how the ball lands successfully back into the launcher every time. Look back at your motion diagrams and think about whether or not one component of motion influences the other component of motion.
Diagram D relates to both B and C because the cart and the ball are both moving at constant velocity and moving at the same speed F.
Calculate the initial velocity of the ball. Think about how your strategy for completing this part can help you towards designing an experiment for the next part of the lab.
3
∆V=
Siena College - General Physics 110
Motion in Two-
Dimensions Lab
1.
Vf y
2
=
Vo y
2
+
2
ay ∆ y
2.
Vo y
2
=
Vf y
2
−
2
ay ∆ y
3.
Voy
=
√
0
−
2
(−
9.8
)
X
0.95
=
4.32
m
/
s
4.
height
=
95
cm
=
0.95
m
Section II -
In this part of the lab, you will design a new qualitative experiment to test the explanation that you devised in Section 1 related to whether or not each component of velocity is dependent on one another.
Equipment: Marbles, projectile launcher, projectile balls, loading rod, larger balls,
meter sticks, 2-meter sticks.
Scientific Ability
Missing
Inadequate
Needs Improvement
Adequate
C2
Is able to design a
reliable experiment that tests the hypothesis
The experiment does not test the hypothesis.
The experiment tests the hypothesis. However, due to the nature of the design, it is very likely that the data will lead to an incorrect judgment.
The experiment tests the hypothesis. However, due to the nature of the design, there is a moderate chance that the data will lead to an inconclusive judgment.
The experiment tests the hypothesis
and has a high likelihood of producing data that
will lead to a conclusive judgment.
C4
Is able to make a reasonable prediction based on a hypothesis
No prediction is made. The experiment is not treated as a testing experiment.
A prediction is made,
but it is identical to the hypothesis OR a prediction is made based on a source unrelated to the hypothesis being tested, or is completely inconsistent with the
hypothesis being tested, OR the prediction is unrelated to the context of the designed experiment.
The prediction follows from the hypothesis, but is flawed because relevant experimental assumptions are not considered and/or the prediction is incomplete or somewhat inconsistent with the
hypothesis and/or the prediction is somewhat inconsistent with the
experiment.
A prediction is made that follows from the
hypothesis, is distinct from the hypothesis, accurately describes the expected outcome of the designed experiment, and incorporates relevant assumptions if needed.
4
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Related Questions
I need the answer as soon as possible
arrow_forward
Task 3
As a part of your role in the motion and dynamics analysis department, you have been asked to
design a mission consists of airplane and boat. The mission target is to deliver a package by the
airplane that must be picked by the boat. You must provide two analysis steps to solve the
problem:
50 m/s
Package
Figure.2: Package of emergency supplies
Part 1
• The airplane traveling horizontally at 50 m/s
• The airplane is 150 m above the sea
1. Define your reference coordinate system
2. Find the x-component of velocity after 2 sec.
3. Find the y-component of velocity after 2 sec.
4. Write the vector of velocity after 2 sec in terms of "I" and "j" components (vector
representation).
arrow_forward
ACTIVITY 2
POSSIBLE AND IMPOSSIBLE COLLISIONS
The table below shows the motion of two objects before collision and the
4 diagrams that represent the motion of the two objects after collision.
Compute for their KE before and after collision to identify whether the
collision is POSSIBLE OR NOT POSSIBLE. Support your answers with a
mathematical solution.
Before Collision
After Collision
Possible or
Impossible
Collision
1 m's
5 mis
8kg
4kg
KE fter
9 mis
4kg
6 mis
KEher=
Skg
8 mis
5 m/s
Skg
KEbefore =
3 mis
9 m's
Skg
4kg
KEafter
Class comm
I mis
Bkg 4kg
a class comn
KEner
arrow_forward
Suggest some likely sources of error that could be responsible for the difference between your measured and predicted values for the horizontal distance traveled by the projectile at the different angles used in this experiment. “Human error” is not acceptable without saying specifically what error the human could have made. “Calculation error” is also not acceptable—if you are worried about whether the calculation is correct, consult with your classmates and/or someone you trust to do the calculation correctly.
PROCEDURE
Part I
Place a marble launcher on the table, oriented so it points straight upward (θ = 90°). Pull the launch mechanism back to the first (nearest) launch position and place a marble into the launcher. Practice quickly releasing the launch mechanism and get a sense for the maximum height the marble will reach after it is launched.
Hold a meter stick beside the marble launcher so that the zero end is beside the marble. Launch the marble and record the maximum…
arrow_forward
Physics
i need answers and work for Part A, Part B, Part C.
arrow_forward
PERFORMANCE TASK #1D IN GENERAL PHYSICS 1
QUARTER 1
Directions: Choose the letter that corresponds to the best answer. Write your answer on the
answer sheet provided.
1. Describe the motion of the ball that is thrown up in the air as illustrated by the picture to the
right? Which of the following is true about the ball's velocity at the highest point B?
A. Its velocity is zero.
B. Its velocity is constant.
2. What is the acceleration of a body that moves at a rate of 2 m/s to 6 m/s in 4s?
A. 0.5 m/s
3. A man runs 30 m long up a hill at an elevation of 30° above the horizontal. What is his vertical displacement?
C. ts velocity is increasing.
D. Its velocity is decreasing.
B. 1 m/s?
C. 1.5 m/s
D. 2 m/s?
B. 26 m
C. 15 m
A. 30 m
4. How long does a high pitched ball with an acceleration of 2.0 m/s² take to go from 10 m/s to 30 m/s?
A. 10 s
5. An airplane lands an initial velocity of 70.0 m/s and then accelerates opposite to the motion at 1.50 m/s² for 40.0 s.
What is its final velocity?
A.…
arrow_forward
I need handwritten or I'll dislike
arrow_forward
In this challenge we will find the angle needed to aim one robot at another as in the diagram below.
The lower robot travels at constant speed vfast and the upper robot travels at constant speed vslow. So both have zero acceleration. The initial vertical distance between them is D. Your challenge is to find the angle needed to cause a collision, the time of the collision, and the location of the collision.Some notes that may help:1. We can treat motion along the horizontal and vertical in the picture separately and write separate equations for them. Let’s call horizontal x and vertical y. 1. We then need to find kinematic equations for x and y for each robot. In other words you need equations for xslow, yslow, xfast, yfast.1. The fast robot has velocity in the x and y directions. The x-component of the robot’s velocity is while the y component is . The initial position of the fast robot is (0,0). So we can write the kinematic equations (eq 1) as and 1. The slow robot has velocity…
arrow_forward
What is tf?
I need help please
arrow_forward
A.) Give more examples of applications of projectile motion.
B.) A boy looking from a building's rooftop observes a small child looping a cord. Which path will the ball take if the cable breaks?
C.) (Refer to the picture)
arrow_forward
e
Learning Activities
Last time, you have learned how to determine if an object is moving or not.
For this module, you will learn how motion can be visualized or illustrated using
tape charts and motion graphs. To help you get ready, perform the task
below:
070
by 1
Read and analyze the following
statements and get ready to answer
the questions listed below:
A jeepney is moving at a rate of 45
kilometers within 0.50 hour before it
stops at a red light. After 5 minutes
the vehicle moves again, but this
time it initially moves at a rate of 15
kilometers for 15 minutes which then
increased to 35 kilometers after
another 15 minutes. The jeepney
then continued to move at the
same speed until it reaches another
Qalloisleseb
stop.
1.
"23930 (263) 21-09-1993 Jeepney DKU-464 and Baliwag
Transit Inc Hino RF NVT-923 (fleet No 2016) in J. Abad Santos
near Solls Street. Tondo, Manila,
Philippines." by express000 is licensed under CC BY-NC-SA 2.0
wepo know?
in the same. Heweld yo
lowe
4. At which…
arrow_forward
sec
Learning Task 4. Doing Detective Work
Read the passage below and answer the guide questions that follows:
Supposed that you are an on-the-job trainee in a private investigating
company tasked to investigate a "hit and run" case. The alleged suspect was
captured by a CCTV camera driving a road leading to the place of incident.
The suspect denied the allegation, saying that he was driving very slowly with
a constant speed. Because of the short time difference when he was caught
by the camera and when the accident happened, he insisted that it was
impossible that he would already be at the place when the crime took place.
But when you are viewing the CCTV footage, you noticed that his car has left
oil spots on the road. When you checked the spots on the site of the accident,
you found out that they are still evident. So, you began to wonder if the spots
can be used to investigate the motion of the car driven by the suspect and
check whether he was telling the truth or not.
0 I
:…
arrow_forward
Only parts D and E. ( i did not know about the first3 parts in the guidelines)
arrow_forward
Learning Task 3
Read the following situations and answer the questions that follow.
1. Raf rides a boat for a fishing trip at 6 kilometer south. After half hour
of waiting, no fishes were caught, so he goes 2 kilometer west. Then
he follows a school of fish 1 kilometer north.
A. How long did he travel?
B. Is the boat's displacement equal to zero?
Write your answers here.
А.
В.
2. The ball rolls from point A (left) to point B (right) at 1.5 meters, as it
reached point B, it rolls back to the starting position.
A.
How far did the ball roll?
B. What is the displacement?
Write your answers here.
А.
В.
arrow_forward
Q. Using the picture given below answer the following questions
N
W
S
Start
E
1. Find the total distance travelled in Path B in the figure if all of the blocks are 80
m on a side.
2. What is the magnitude of the displacement of Path D if all blocks are 80 m on a
side?
3. What is the total distance travelled for Path D if each block is 140 m on a side?
4. Find the magnitude of the displacement for Path B in the figure if all of the
blocks are 120 m on a side.
arrow_forward
Please no hand writing solution
arrow_forward
toright
or
ht
Enter
eft
cente
Particle Motion Practice
noitoM isenilite
Peanut the kitten pretty much has run of the basement. Her
favorite pastime is batting a ball along one of the basement
walls. The wall is 20 feet long with the exact center of the
wall position 0, the left edge of the wall position -10, and
the right edge of the wall position 10. During a particularly
frisky playtime Peanut's position along the wall is given by
the equation s(t)= t³ −3t² −2t+1
oniasenpeb ei (1)
1) Evaluate and explain what is meant by s(0), s(2), and s(4)
2) Find her velocity and speed at times t=1 and t=3.5
seconds. Give her average velocity over the interval [1,3.5]
3) On the interval [0,4] when is she decelerating?
pniar
(v
arrow_forward
Connect to Internet !! to be notified about an update when new
papers are available, stay connected to the internet
8.
QUESTIONS
Write neatly and legibly.
Copyright reserved
(15070402)
QUESTION 1: DYNAMICS
Differentiate between a scalar quantity and a vector quantity.
1.1
1.2
Define the term velocity
1.3
ANSWERS
Please turn over
The diagram below describes the motion of a body taking place in a straight
line.
Displacement (m)
80
0
6
10
16 18
-40-
Time(s)
-80
-120-
1.3.1
Determine the velocity during the first 8 seconds.
(2)
1.3.2
Describe the movement between the 8th and 12th second.
(1)
1.3.3
Determine the total distance travelled from the diagram.
(1)
1.3.4
Determine the displacement from the diagram.
(2)
1.4
A brick is dropped vertically downwards from the top of a building at 3 m/s to
reach the ground after 5 s.
Calculate the height of the building.
(3)
1.5
An object is accelerated uniformly from 35 km/h to 105 km/h in 12 s.
Calculate the acceleration of the object.
(3)
[15]…
arrow_forward
Instructions
Timed Test
This test has a time limit of 30 minutes.This test will save and submit autornatically whe
Wamings appear when half the time, 5 minutes, 1 minute, and 30 seconds remain.
Multiple Attempts Not allowed. This test can only be taken once.
Force Completion This test can be saved and resumed at any point until time has expired. The timer will cc
Remaining Time: 20 minutes, 53 seconds.
A Question Completion Status:
1
4.
A Moving to another question will save this response.
Question 2
"If the voltage is increased, then the electrical energy will be (keeping Resistance and time duration fixed)"
O Increased
O Decreased
O Same
O None of these
A Moving to another question will save this response.
Take Test: FL21_Phy.
FUJITSU
F6
F7
F8
F9
F10
F11
F12
Prt Scr
Sys Rq
ECO
&
6.
7
V
9
Y!
arrow_forward
Dynamics of Rigid Bodies
Cars A and B approached each other on a straight road from points 460 m apart. Car A has an initial speed of 70 kph and is decelerating at the rate of 0.40 m/s^2. Car B has an initial speed of 20 kph and is accelerating at the rate of 0.30 m/s^2. When will the cars meet and how far will each have traveled? Draw the figureproperly. No figure no point.
arrow_forward
I did a lab based Projectile Motion and they ask me this question
Following the definitions of direct and inverse proportionality earlier, discuss why this equation shows that your answers for initial velocity and gravity are correct.
* Note that this range equation only works if y0 = yf
I think is because of the no air resistance but im not sure can you help me this one I don't want to know if I'm right or wrong?
arrow_forward
I need help on this entire thing?
arrow_forward
A bowling ball of mass 7. 5kg travelling at 10 m/s rolls off a horizontal table 1.0m high. Ignore air resistance.
arrow_forward
1.5 m
B
Vo
A
65°
Referring to the figure above:
a. Write the equation that represents the time it takes for the ball to reach point B from point A
b. What is the magnitude of Vo
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill
Related Questions
- I need the answer as soon as possiblearrow_forwardTask 3 As a part of your role in the motion and dynamics analysis department, you have been asked to design a mission consists of airplane and boat. The mission target is to deliver a package by the airplane that must be picked by the boat. You must provide two analysis steps to solve the problem: 50 m/s Package Figure.2: Package of emergency supplies Part 1 • The airplane traveling horizontally at 50 m/s • The airplane is 150 m above the sea 1. Define your reference coordinate system 2. Find the x-component of velocity after 2 sec. 3. Find the y-component of velocity after 2 sec. 4. Write the vector of velocity after 2 sec in terms of "I" and "j" components (vector representation).arrow_forwardACTIVITY 2 POSSIBLE AND IMPOSSIBLE COLLISIONS The table below shows the motion of two objects before collision and the 4 diagrams that represent the motion of the two objects after collision. Compute for their KE before and after collision to identify whether the collision is POSSIBLE OR NOT POSSIBLE. Support your answers with a mathematical solution. Before Collision After Collision Possible or Impossible Collision 1 m's 5 mis 8kg 4kg KE fter 9 mis 4kg 6 mis KEher= Skg 8 mis 5 m/s Skg KEbefore = 3 mis 9 m's Skg 4kg KEafter Class comm I mis Bkg 4kg a class comn KEnerarrow_forward
- Suggest some likely sources of error that could be responsible for the difference between your measured and predicted values for the horizontal distance traveled by the projectile at the different angles used in this experiment. “Human error” is not acceptable without saying specifically what error the human could have made. “Calculation error” is also not acceptable—if you are worried about whether the calculation is correct, consult with your classmates and/or someone you trust to do the calculation correctly. PROCEDURE Part I Place a marble launcher on the table, oriented so it points straight upward (θ = 90°). Pull the launch mechanism back to the first (nearest) launch position and place a marble into the launcher. Practice quickly releasing the launch mechanism and get a sense for the maximum height the marble will reach after it is launched. Hold a meter stick beside the marble launcher so that the zero end is beside the marble. Launch the marble and record the maximum…arrow_forwardPhysics i need answers and work for Part A, Part B, Part C.arrow_forwardPERFORMANCE TASK #1D IN GENERAL PHYSICS 1 QUARTER 1 Directions: Choose the letter that corresponds to the best answer. Write your answer on the answer sheet provided. 1. Describe the motion of the ball that is thrown up in the air as illustrated by the picture to the right? Which of the following is true about the ball's velocity at the highest point B? A. Its velocity is zero. B. Its velocity is constant. 2. What is the acceleration of a body that moves at a rate of 2 m/s to 6 m/s in 4s? A. 0.5 m/s 3. A man runs 30 m long up a hill at an elevation of 30° above the horizontal. What is his vertical displacement? C. ts velocity is increasing. D. Its velocity is decreasing. B. 1 m/s? C. 1.5 m/s D. 2 m/s? B. 26 m C. 15 m A. 30 m 4. How long does a high pitched ball with an acceleration of 2.0 m/s² take to go from 10 m/s to 30 m/s? A. 10 s 5. An airplane lands an initial velocity of 70.0 m/s and then accelerates opposite to the motion at 1.50 m/s² for 40.0 s. What is its final velocity? A.…arrow_forward
- I need handwritten or I'll dislikearrow_forwardIn this challenge we will find the angle needed to aim one robot at another as in the diagram below. The lower robot travels at constant speed vfast and the upper robot travels at constant speed vslow. So both have zero acceleration. The initial vertical distance between them is D. Your challenge is to find the angle needed to cause a collision, the time of the collision, and the location of the collision.Some notes that may help:1. We can treat motion along the horizontal and vertical in the picture separately and write separate equations for them. Let’s call horizontal x and vertical y. 1. We then need to find kinematic equations for x and y for each robot. In other words you need equations for xslow, yslow, xfast, yfast.1. The fast robot has velocity in the x and y directions. The x-component of the robot’s velocity is while the y component is . The initial position of the fast robot is (0,0). So we can write the kinematic equations (eq 1) as and 1. The slow robot has velocity…arrow_forwardWhat is tf? I need help pleasearrow_forward
- A.) Give more examples of applications of projectile motion. B.) A boy looking from a building's rooftop observes a small child looping a cord. Which path will the ball take if the cable breaks? C.) (Refer to the picture)arrow_forwarde Learning Activities Last time, you have learned how to determine if an object is moving or not. For this module, you will learn how motion can be visualized or illustrated using tape charts and motion graphs. To help you get ready, perform the task below: 070 by 1 Read and analyze the following statements and get ready to answer the questions listed below: A jeepney is moving at a rate of 45 kilometers within 0.50 hour before it stops at a red light. After 5 minutes the vehicle moves again, but this time it initially moves at a rate of 15 kilometers for 15 minutes which then increased to 35 kilometers after another 15 minutes. The jeepney then continued to move at the same speed until it reaches another Qalloisleseb stop. 1. "23930 (263) 21-09-1993 Jeepney DKU-464 and Baliwag Transit Inc Hino RF NVT-923 (fleet No 2016) in J. Abad Santos near Solls Street. Tondo, Manila, Philippines." by express000 is licensed under CC BY-NC-SA 2.0 wepo know? in the same. Heweld yo lowe 4. At which…arrow_forwardsec Learning Task 4. Doing Detective Work Read the passage below and answer the guide questions that follows: Supposed that you are an on-the-job trainee in a private investigating company tasked to investigate a "hit and run" case. The alleged suspect was captured by a CCTV camera driving a road leading to the place of incident. The suspect denied the allegation, saying that he was driving very slowly with a constant speed. Because of the short time difference when he was caught by the camera and when the accident happened, he insisted that it was impossible that he would already be at the place when the crime took place. But when you are viewing the CCTV footage, you noticed that his car has left oil spots on the road. When you checked the spots on the site of the accident, you found out that they are still evident. So, you began to wonder if the spots can be used to investigate the motion of the car driven by the suspect and check whether he was telling the truth or not. 0 I :…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill