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HW3
HW3
Due: 11:59pm on Monday, October 13, 2014
To understand how points are awarded, read the Grading Policy for this assignment.
Tactics Box 3.3 Determining the Components of a Vector
Learning Goal:
To practice Tactics Box 3.3 Determining the component of a vector.
When a vector A⃗ is decomposed into component vectors A⃗x and A⃗y parallel to the coordinate axes, we can
describe each component vector with a single number (a scalar) called the component. This Tactics Box describes
how to determine the x component and y component of vector A⃗, denoted Ax and Ay .
TACTICS BOX 3.3
Determining the components of a vector
1. The absolute value |Ax | of the x component Ax is the magnitude of the component vector A⃗x .
2. The sign of Ax is positive if A⃗x points in the positive x direction; it is negative if A⃗x points in the
negative x direction.
3. The y component Ay is determined similarly.
Part A
What is the magnitude of the component vector A⃗x shown in the figure?
Express your answer in meters to two significant
figures.
ANSWER:
|A x |
=
m
Part B
What is the sign of the y component Ay of vector A⃗ shown in the figure?
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ANSWER:
positive
negative
Part C
This question will be shown after you complete previous question(s).
Components of Vectors
Shown is a 10 by 10 grid, with coordinate axes x and y
.
The grid runs from -5 to 5 on both axes. Drawn on this grid
are four vectors, labeled A⃗ through D⃗ . This problem will
ask you various questions about these vectors. All
answers should be in decimal notation, unless otherwise
specified.
Part A
What is the x component of A⃗?
Express your answer to two significant figures.
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You did not open hints for this part.
ANSWER:
Ax
=
Part B
What is the y component of A⃗?
Express your answer to the nearest integer.
ANSWER:
Ay
=
Part C
What is the y component of B⃗ ?
Express your answer to the nearest integer.
You did not open hints for this part.
ANSWER:
By
=
Part D
What is the x component of C ⃗?
Express your answer to the nearest integer.
You did not open hints for this part.
ANSWER:
Cx
=
The following questions will ask you to give both components of vectors using the ordered pairs method. In this
method, the x component is written first, followed by a comma, and then the y component. For example, the
components of A⃗ would be written 2.5,3 in ordered pair notation.
The answers below are all integers, so estimate the components to the nearest whole number.
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Part E
In ordered pair notation, write down the components of vector B⃗ .
Express your answers to the nearest integer.
ANSWER:
Bx
, By =
Part F
In ordered pair notation, write down the components of vector D⃗ .
Express your answers to the nearest integer.
ANSWER:
Dx
, Dy =
Part G
What is true about B⃗ and D⃗ ? Choose from the pulldown list below.
ANSWER:
They have different components and are not the same vectors.
They have the same components but are not the same vectors.
They are the same vectors.
Problem 3.15
A wildlife researcher is tracking a flock of geese. The geese fly 4.5
and fly another 5.0 km .
km
due west, then turn toward the north by 50∘
Part A
How far west are they of their initial position?
Express your answer to two significant figures and include the appropriate units.
ANSWER:
dw
=
Part B
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What is the magnitude of their displacement?
Express your answer to two significant figures and include the appropriate units.
ANSWER:
d
=
Problem 3.5
A position vector with magnitude 20
m
points to the right and up. Its x-component is 16
m
.
Part A
What is the value of its y-component?
Express your answer to two significant figures and include the appropriate units.
ANSWER:
y
=
Problem 3.2
Part A
Draw the vector C ⃗
⃗
⃗
= A +B
.
ANSWER:
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Part B
Draw the vector D⃗
⃗
⃗
= A −B
.
ANSWER:
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Problem 3.1
Part A
Draw the vector D⃗
⃗
⃗
= A +B
.
ANSWER:
Part B
Draw the vector C ⃗
⃗
⃗
= A −B
.
ANSWER:
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Vector Magnitude and Direction Conceptual Question
A man out walking his dog makes one complete pass around a perfectly square city block. He starts at point A and
walks clockwise around the block.
⃗
⃗
Let r AB
be the displacement vector from A to B, r BC
be the displacement vector from B to C, etc.
Part A
⃗
Which of the following vectors is equal to r AB
?
You did not open hints for this part.
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ANSWER:
⃗
r BC
only
⃗
r CD
only
⃗
r DA
only
All of the above
None of the above
Part B
⃗
Which of the following vectors is equal to −r AB
?
ANSWER:
⃗
r BC
only
⃗
r CD
only
⃗
r DA
only
All of the above
None of the above
Part C
⃗
Which of the following vectors is equal to r AB
⃗
− r DA
?
You did not open hints for this part.
ANSWER:
⃗
⃗
−(r CD
+ r DA
)
⃗
⃗
r AB
+ r BC
only
⃗
⃗
r BC
− r CD
only
only
All of the above
None of the above
Adding and Subtracting Vectors Conceptual Question
Six vectors (A to F) have the magnitudes and directions indicated in the figure.
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Part A
Which two vectors, when added, will have the largest (positive) x component?
You did not open hints for this part.
ANSWER:
C and E
E and F
A and F
C and D
B and D
Part B
Which two vectors, when added, will have the largest (positive) y component?
You did not open hints for this part.
ANSWER:
C and D
A and F
E and F
A and B
E and D
Part C
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Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest
magnitude?
You did not open hints for this part.
ANSWER:
A and F
A and E
D and B
C and D
E and F
Vector Addition Ranking Task
Six vectors (a⃗ through f ⃗) have the magnitudes and directions indicated in the figure.
Part A
Rank the vector combinations on the basis of their magnitude.
Rank from largest to smallest. To rank items as equivalent, overlap them.
You did not open hints for this part.
ANSWER:
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Part B
Rank the vector combinations on the basis of their angle, measured counterclockwise from the positive x axis.
Vectors parallel to the positive x axis have an angle of 0∘ . All angle measures fall between 0∘ and 360∘ .
Rank from largest to smallest. To rank items as equivalent, overlap them.
You did not open hints for this part.
ANSWER:
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Adding Scalar Multiples of Vectors Graphically
Draw the vectors indicated. You may use any extra (unlabeled) vectors that are helpful; but, keep in mind that the
unlabeled vectors should be deleted before submitting your answer.
Part A
Draw the vector C ⃗
⃗
⃗
= A + 2B
.
The length and orientation of the vector will be graded. The location of the vector is not important.
You did not open hints for this part.
ANSWER:
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Part B
Draw the vector C ⃗
⃗
⃗
= 1.5A − 3B
.
The length and orientation of the vector will be graded. The location of the vector is not important.
You did not open hints for this part.
ANSWER:
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Part C
Draw the vector C ⃗
⃗
⃗
= 0.5A + 2B
.
The length and orientation of the vector will be graded. The location of the vector is not important.
You did not open hints for this part.
ANSWER:
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Tactics Box 3.1 Subtracting Vectors
Learning Goal:
To practice Tactics Box 3.1 Subtracting vectors
Vector subtraction has some similarities to the subtraction of two scalar quantities. With numbers, subtraction is the
same as the addition of a negative number. For example, 5 − 3 is the same as 5 + (−3) . Similarly,
⃗
⃗
⃗
⃗
A − B = A + (−B)
. We can use the rules for vector addition and the fact that −B⃗ is a vector opposite in direction
to B⃗ to form rules for vector subtraction, as explained in this Tactics Box.
TACTICS BOX 3.1
Subtracting vectors
To subtract B⃗ from A⃗ perform these steps:
1. Draw A⃗.
2. Place the tail of −B⃗ at the tip of A⃗.
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3. Draw an arrow from the tail of A⃗ to the tip of −B⃗ . This is vector A⃗ − B⃗ .
Part A
Find vector C ⃗ = A⃗ − B⃗ by following the steps in the Tactics Box above. Make certain to draw −B⃗ with the
correct orientation.
ANSWER:
Part B
Find vector F ⃗ = D⃗ − E⃗ by following the steps in the Tactics Box above. Make certain to draw −E⃗ with the
correct orientation.
ANSWER:
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± Resolving Vector Components with Trigonometry
Often a vector is specified by a magnitude and a direction;
for example, a rope with tension T ⃗ exerts a force of
magnitude T in a direction 35∘ north of east. This is a
good way to think of vectors; however, to calculate results
with vectors, it is best to select a coordinate system and
manipulate the components of the vectors in that
coordinate system.
Part A
Find the components of the vector A⃗ with length a = 1.00 and angle α=20.0∘ with respect to the x axis as
shown.
Enter the x component followed by the y component, separated by a comma.
You did not open hints for this part.
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ANSWER:
⃗
=
A
Part B
Find the components of the vector B⃗ with length b = 1.00 and angle β=20.0∘ with respect to the x axis as
shown.
Enter the x component followed by the y component, separated by a comma.
You did not open hints for this part.
ANSWER:
⃗
B
=
Part C
Find the components of the vector C ⃗ with length c = 1.00 and angle ϕ
=
35.0∘ as shown.
Enter the x component followed by the y component, separated by a comma.
You did not open hints for this part.
ANSWER:
C
⃗
=
± Biking Vectors
A student bikes to school by traveling first d N = 1.00miles north, then d W = 0.500miles west, and finally
d S = 0.100miles south.
Part A
If a bird were to start out from the origin (where the student starts) and fly directly (in a straight line) to the
school, what distance d b would the bird cover?
Express your answer in miles.
You did not open hints for this part.
ANSWER:
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db
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=
miles
Part B
This question will be shown after you complete previous question(s).
Part C
This question will be shown after you complete previous question(s).
Part D
This question will be shown after you complete previous question(s).
Part E
This question will be shown after you complete previous question(s).
Part F
This question will be shown after you complete previous question(s).
Problem 3.8
Josh is climbing up a steep 32∘ slope, moving at a steady 0.90
m/s
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along the ground in .
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Part A
How many meters of elevation does he gain in one minute of this climb?
Express your answer to two significant figures and include the appropriate units.
ANSWER:
d
=
Score Summary:
Your score on this assignment is 0.0%.
You received 0 out of a possible total of 105 points.
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