PHYS-2211-A-SPRING24.903690020.2211HW1-2
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School
Georgia Institute Of Technology *
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Course
2211
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
13
Uploaded by serimegha
2211HW1
closes 01/26/2024 at 11:59pm EST
Megha Shivani Seri (903690020)
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for credit.
Problem 1
(1 point)
If one vector is subtracted from a second vector to yield a resultant vector of magnitude A, at least
one of the first two vectors must have a magnitude greater than A.
Is this statement true or false?
•
A. False
•
B. True
Problem 2
(1 point)
1. If one vector is subtracted from a second vector to yield a resultant vector of zero magnitude,
the two initial vectors are necessarily equal.
2. The x component of a vector cannot be greater than the magnitude of that vector.
Which combination of statements is correct?
•
A. Only (1)
•
B. Only (2)
•
C. Both
•
D. Neither
Problem 3
(1 point)
If
⃗a
= ( 25 ˆ
x
+ 15 ˆ
y
) and
⃗
b
is as shown below, what is the magnitude of the sum of these two
vectors?
Page 1
Problem 4
(1 point)
Vectors
⃗
A
and
⃗
B
are as shown. What is the magnitude of vector
⃗
C
if
⃗
C
=
⃗
A
−
⃗
B
?
Page 2
Problem 5
(1 point)
If
⃗
A
= ( 4
ˆ
i
+ 14
ˆ
j
) and
⃗
B
= ( -13
ˆ
i
+ 13
ˆ
j
), what is the magnitude of the vector
⃗
C
= 5
⃗
A
- 5
⃗
B
?
Problem 6
(1 point)
If
|
⃗a
|
= 13 m,
|
⃗
b
|
= 17 m,
α
= 29 degrees,
β
= 85 degrees, and
⃗
c
=
⃗a
−
⃗
b
, determine the magnitude
of
⃗
c
.
Page 3
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Page 4
Problem 7
(1 point)
A)
A
+
C
=
B
B)
B
=
C
−
A
C)
B
−
A
=
C
D)
A
−
B
=
C
Which of these corresponds to the diagram?
•
A. A
•
B. B
•
C. C
•
D. D
Page 5
Problem 8
(1 point)
A)
A
−
B
=
C
B)
C
−
A
=
B
C)
C
=
A
+
B
D)
C
=
B
−
A
Which of these corresponds to the diagram?
•
A. A
•
B. B
•
C. C
•
D. D
Problem 9
(1 point)
Introduction
Imagine that you have a tennis ball and a baseball at different locations. The center of the tennis
ball is at ‘
<
-3,-1,0
>
‘ m, and the center of the baseball is at ‘
<
3,5,0
>
‘ m.
The position vector of the baseball is
⃗
B
. The position vector of the tennis ball is
⃗
T
. The position
vector of the tennis ball relative to the baseball is
⃗
r
.
Graphing Vectors
Page 6
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Image [/A/B/C] best corresponds to the described geometry.
Calculating Vectors
(For all blanks below, enter a formula or a numeric answer with three or more decimal places.)
Find
⃗
r
by reading its value from the picture.
⃗
r
=
<
,
,
>
Calculate the unit vector ˆ
r
.
ˆ
r
=
<
,
,
>
Calculate the magnitudes of the following vectors:
|
⃗
B
|
:
|
⃗
T
|
:
|
⃗
r
|
:
Problem 10
(1 point)
A particle moving in the xy plane undergoes three consecutive displacement given by
⃗
A
= (4
ˆ
i
+ 1
ˆ
j
),
⃗
B
= (
−
5
ˆ
i
+ 4
ˆ
j
), and
⃗
C
= (5
ˆ
j
) with distances measured in meters. The resultant displacement is
⃗
R
=
⃗
A
+
⃗
B
+
⃗
C
. What is the magnitude of
⃗
R
?
Page 7
Select the correct answer (in meters).
•
A. 10.050
•
B. 17.085
•
C. 5.025
•
D. 8.040
Problem 11
(1 point)
Is this statement true or false?
The sum of the x and y components of a vector can be greater than the magnitude of that vector.
•
A. True
•
B. False
Problem 12
(1 point)
A yellow jacket is initially at location
⃗
r
i
=
<
55
,
50
,
−
50
>
and 0.5 seconds later is observed at
⃗
r
f
=
<
−
35
,
−
55
,
−
20
>
.
1.) Determine the average velocity
⃗v
avg
of the yellow jacket
<
,
,
>
m/s
2.) Calculate the unit vector ˆ
v
avg
that points in the direction of the average velocity you found in
part 1
<
,
,
>
3.) Some time later the average velocity is found to have a magnitude of 20 m/s, lie in the xy plane,
and make an angle of 50 degrees with respect to the +x axis (measured counterclockwise). Calculate
the unit vector of this average velocity, ˆ
v
avg
<
,
,
>
Problem 13
(1 point)
A hockey puck slides across an ice rink. Take the origin of coordinates to be the center of the rink,
and let the rink lie in the xy plane. At the time t = 0.0 seconds a hockey puck is observed to be at
Page 8
location
<
7, 0, -4
>
m. At time t = 0.4 seconds the puck is observed at location
<
-2, 0, 4
>
m.
1. What is the average velocity of the hockey puck during this time interval?
⃗v
avg
x
=
⃗v
avg
y
=
⃗v
avg
z
=
1. What is the magnitude of the average velocity?
|
⃗v
avg
|
=
1. What is the unit vector in the direction of the velocity?
ˆ
v
avg
x
=
ˆ
v
avg
y
=
ˆ
v
avg
z
=
Problem 14
(1 point)
Page 9
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A ball kicked into the air moves along the path shown above;
it is at point A and then
later at point B.
?
1. Which arrow indicates the direction of the ball’s instantaneous velocity at point B?
?
1. Which arrow indicates the direction of the ball’s average velocity from point A to point B?
?
1. Which arrow indicates the direction of the change in the ball’s momentum from point A to
point B?
Problem 15
(1 point)
The position of a particle moving along the x-axis is given by
x
= (20 + 16
t
−
8
t
2
) meters, where
t
is in seconds. What is the average velocity during the time interval
t
= 4 s to
t
= 7 s ?
m/s
Problem 16
(1 point)
Page 10
An object’s initial velocity
⃗v
i
and final velocity
⃗v
f
are shown below. Using the numbered direction
arrows shown, indicate (by number) which arrow best represents the direction of the quantities
listed below.
If the quantity has zero magnitude or cannot be determined, indicate using the
corresponding number listed.
?
1. The change in momentum ∆
⃗
p
?
2. The initial position vector
⃗
r
i
?
3. The net force
⃗
F
net
?
4. The change in velocity ∆
⃗v
?
5. The acceleration
⃗a
Problem 17
(1 point)
An object moves from location D to location F on a trajectory (dotted line) in the direction indicated;
arrows representing the velocities at locations D, E, and F are also indicated.
Page 11
Using the numbered direction arrows shown, indicate (by number) which direction arrow best
represents the direction of the quantities listed below. If the quantity has zero magnitude or cannot
be determined, indicate this with a 9 or 10, respectively.
?
1. The change in velocity between location D and location F:
?
2. The change in position (the displacement) between location D and location F:
?
3. The average net force between location D and location E:
?
4. The average net force between location D and location F:
?
5. The change in velocity between location D and location E:
?
6. The position vector at location E:
?
7. The position vector at location D:
?
8. The change in momentum between location D and location E:
?
9. The change in momentum between location D and location F:
?
10. The change in position (the displacement) between location D and location E:
Problem 18
(1 point)
Is the following statement true or false?
|
⃗
A
| − |
⃗
B
|
=
|
⃗
A
−
⃗
B
|
.
•
A. True
Page 12
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•
B. False
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