lavallo (jhl936) – Homework 04 – florin – (58140)
1
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printout
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have
16
questions.
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before answering.
001
(part 1 of 2) 10.0 points
Two vectors
A
and
B
, are lying in the
xy
plane and given by
A
=
A
x
i
+
A
y
j
B
=
B
x
i
+
B
y
j
.
where
A
x
= 2
.
67 m,
A
y
= 0
.
979 m,
B
x
=
4
.
2 m,
B
y
=
−
8
.
58 m. Let
R
=
A
+
B
.
Find the magnitude of
R
.
Correct answer: 10
.
2456 m.
Explanation:
The resultant vector
R
is given by
R
=
A
+
B
= (
A
x
i
+
A
y
j
) + (
B
x
i
+
B
y
j
)
= (
A
x
+
B
x
)
i
+ (
A
y
+
B
y
)
j
= (2
.
67 m + 4
.
2 m)
i
+ (0
.
979 m + (
−
8
.
58 m))
j
= 6
.
87 m
i
+ (
−
7
.
601 m)
j
.
The magnitude,
R
, of
R
is
R
=
radicalBig
R
2
x
+
R
2
y
=
radicalBig
(6
.
87 m)
2
+ (
−
7
.
601 m)
2
= 10
.
2456 m
.
002
(part 2 of 2) 10.0 points
Find the angle
θ
that the vector
R
makes from
the positive
x
axis. Choose your answer to be
between
−
180
◦
and +180
◦
. The positive an
gular direction is counter clockwise measured
from the
x
axis.
Correct answer:
−
47
.
8918
◦
.
Explanation:
The point is in the fourth quadrant of the
coordinate system, so the angle
θ
that the
vector
R
=
A
+
B
makes with the positive
x
axis is
θ
= arctan
R
y
R
x
= arctan
(
−
7
.
601 m)
(6
.
87 m)
= (
−
47
.
8918
◦
)
=
−
47
.
8918
◦
.
003
(part 1 of 2) 10.0 points
Consider two vectors
vector
A
and
vector
B
and their re
sultant
vector
A
+
vector
B
. The magnitudes of the vectors
vector
A
and
vector
B
are, respectively, 14
.
5 and 6
.
1 and
they act at 65
◦
to each other.
vector
A
vector
B
vector
A
+
vector
B
Find the magnitude of the resultant vector
vector
A
+
vector
B
.
Correct answer: 17
.
9505.
Explanation:
Let :
a
= 14
.
5
,
b
= 6
.
1
,
and
θ
= 65
◦
.
b
γ
r
a
γ
= 180
◦
−
65
◦
= 115
◦
,
so applying the law of cosines,
r
2
=
a
2
+
b
2
−
2
a b
cos
γ
= (14
.
5)
2
+ (6
.
1)
2
−
2 (14
.
5) (6
.
1) cos 115
◦
= 322
.
221
r
=
√
322
.
221 =
17
.
9505
.
004
(part 2 of 2) 10.0 points
Find the angle between the direction of the
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lavallo (jhl936) – Homework 04 – florin – (58140)
2
resultant vector
A
+
B
and the direction of
the vector
A
.
Correct answer: 17
.
9378
◦
.
Explanation:
a
r
β
γ
b
Applying the law of sines,
b
sin
β
=
r
sin
γ
sin
β
=
b
sin
γ
r
β
= arcsin
parenleftbigg
b
sin
γ
r
parenrightbigg
= arcsin
parenleftbigg
6
.
1 sin 115
◦
17
.
9505
parenrightbigg
=
17
.
9378
◦
.
005
(part 1 of 2) 10.0 points
Vector
vector
A
has
x
and
y
components of
−
20 cm
and 6
.
7 cm
,
respectively; vector
vector
B
has
x
and
y
components of 19
.
9 cm and
−
20 cm
,
respec
tively.
If
vector
A
−
vector
B
+3
vector
C
= 0, what is the
x
component
of
vector
C
?
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 Spring '10
 Florin
 Vector Space, Dot Product, Acceleration, Correct Answer, Euclidean vector, Vector Motors

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