magalhaes (bam2734) – Homework #3 – Erskine – (58200)
1
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22
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001
(part 1 of 2) 10.0 points
Two
points
have
cartesian
coordinates
(8
.
3 m
,
−
10 m) and (
−
10 m
,
4
.
9 m).
Find the distance between these points.
Correct answer: 23
.
5987 m.
Explanation:
Let :
x
1
= 8
.
3 m
,
y
1
=
−
10 m
,
x
2
=
−
10 m
,
and
y
2
= 4
.
9 m
.
The distance is
d
=
radicalBig
(
x
2
−
x
1
)
2
+ (
y
2
−
y
1
)
2
=
{
[
−
10 m
−
(8
.
3 m)]
2
+ [4
.
9 m
−
(
−
10 m)]
2
}
1
/
2
=
23
.
5987 m
.
002
(part 2 of 2) 10.0 points
What is the angle between the line connect
ing the two points and the
x
axis (measured
counterclockwise from the
x
axis and within
the limits of
−
180
◦
to +180
◦
)?
Correct answer: 140
.
847
◦
.
Explanation:
The angle is
θ
= arctan
parenleftbigg
y
2
−
y
1
x
2
−
x
1
parenrightbigg
= arctan
bracketleftbigg
4
.
9 m
−
(
−
10 m)
−
10 m
−
(8
.
3 m)
bracketrightbigg
=
140
.
847
◦
.
(
−
10, 4
.
9)
(8
.
3,
−
10)
θ
003
10.0 points
Two airplanes leave an airport at the same
time.
The velocity of the first airplane is
680 m
/
h at a heading of 37
.
9
◦
. The velocity
of the second is 640 m
/
h at a heading of 183
◦
.
How far apart are they after 2
.
9 h?
Correct answer: 3652 m.
Explanation:
Let :
v
1
= 680 m
/
h
,
θ
1
= 37
.
9
◦
,
v
2
= 640 m
/
h
,
and
θ
2
= 183
◦
.
Under constant velocity, the displacement
for each plane in the time
t
is
d
=
v t.
These displacements form two sides of a tri
angle with the angle
α
=
θ
2
−
θ
1
= 145
.
1
◦
between them. The law of cosines applies for
SAS, so the distance between the planes is
d
=
radicalBig
d
2
1
+
d
2
2
−
2
d
1
d
2
cos
α .
Since
2
d
1
d
2
cos
α
= 2 (1972 m) (1856 m) cos 145
.
1
◦
=
−
6
.
00357
×
10
6
m
2
,
then
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magalhaes (bam2734) – Homework #3 – Erskine – (58200)
2
d
=
bracketleftbig
(1972 m)
2
+ (1856 m)
2
−−
6
.
00357
×
10
6
m
2
bracketrightbig
1
/
2
=
3652 m
.
004
10.0 points
A vector of magnitude 2 CANNOT be
added to a vector of magnitude 3 so that
the magnitude of the resultant is
1.
2
2.
3
3.
more information is needed.
4.
0
correct
5.
5
6.
1
Explanation:
The resultant vector of two added vectors
can be zero only when the two vectors have
the same magnitudes and opposite directions
or are both zeroes.
005
(part 1 of 2) 10.0 points
Consider two vectors
vector
A
and
vector
B
and their resul
tant
vector
A
+
vector
B
. The magnitudes of the vectors
vector
A
and
vector
B
are, respectively, 14 and 8
.
2 and they
act at 75
◦
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
.
9629.
Explanation:
Let :
a
= 14
,
b
= 8
.
2
,
and
θ
= 75
◦
.
b
γ
r
a
γ
= 180
◦
−
75
◦
= 105
◦
,
so applying the law of cosines,
r
2
=
a
2
+
b
2
−
2
a b
cos
γ
= (14)
2
+ (8
.
2)
2
−
2 (14) (8
.
2) cos 105
◦
= 322
.
665
r
=
√
322
.
665 =
17
.
9629
.
006
(part 2 of 2) 10.0 points
Find the angle between the direction of the
resultant vector
A
+
B
and the direction of
the vector
A
.
Correct answer: 26
.
164
◦
.
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 Spring '09
 erskine
 Cartesian Coordinate System, Work, René Descartes, Correct Answer, Erskine

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