huynh (hph268) – HW #2 – clark – (56485)
1
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001
(part 1 of 2) 10.0 points
A physics book is moved once around the
perimeter of a table of dimensions 1 m by 3
m.
If the book ends up at its initial position,
what is the magnitude of its displacement?
1.
6 m
2.
3 m
3.
2 m
4.
4 m
5.
1 m
6.
5 m
7.
None of these
8.
7 m
9.
0 m
correct
10.
8 m
Explanation:
Since its final position is the same as its
initial position, the displacement is 0.
002
(part 2 of 2) 10.0 points
What is the distance traveled?
1.
1 m
2.
6 m
3.
None of these
4.
3 m
5.
4 m
6.
7 m
7.
5 m
8.
0 m
9.
2 m
10.
8 m
correct
Explanation:
The distance traveled is the perimeter of
the table:
d
= 2
ℓ
+ 2
w
= 2 (1 m) + 2 (3 m)
= 8 m
.
003
(part 1 of 2) 10.0 points
Consider the two vectors
vector
M
= (
a, b
) =
a
ˆ
ı
+
b
ˆ
and
vector
N
= (
c, d
) =
c
ˆ
ı
+
d
ˆ
.
What is the value of the scalar product
vector
M
·
vector
M
?
1.
a

b
2.
a
2

2
a b
+
b
2
3.

2
a b
4.
a
2
+
b
2
correct
5.
radicalbig
a
2
+
b
2
6.
a
+
b
7.
2
a b
8.
a
2
+ 2
a b
+
b
2
9.
a
2

b
2
Explanation:
ˆ
ı
·
ˆ
ı
= ˆ
·
ˆ
= 1 and ˆ
·
ˆ
ı
= ˆ
ı
·
ˆ
= 0, so
vector
M
·
vector
M
= (
a
ˆ
ı
+
b
ˆ
)
·
(
a
ˆ
ı
+
b
ˆ
)
=
a
2
(ˆ
ı
·
ˆ
ı
) +
b a
(ˆ
·
ˆ
ı
)
+
a b
(ˆ
ı
·
ˆ
) +
b
2
(ˆ
·
ˆ
)
=
a
2
+
b
2
.
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huynh (hph268) – HW #2 – clark – (56485)
2
004
(part 2 of 2) 10.0 points
What is the value of the scalar product
vector
M
·
vector
N
?
1.
a
2
+
b
2
+
c
2
+
d
2
2.
a d

b c
3.
a d
+
b c
4.
a b c d
5.
a c
+
b d
correct
6.
a c

b d
7.
a b
+
c d
8.
radicalbig
a
2
+
b
2
+
radicalbig
c
2
+
d
2
9.
a b

c d
Explanation:
vector
M
·
vector
N
= (
a
ˆ
ı
+
b
ˆ
)
·
(
c
ˆ
ı
+
d
ˆ
)
=
a c
(ˆ
ı
·
ˆ
ı
) +
b c
(ˆ
·
ˆ
ı
)
+
a d
(ˆ
ı
·
ˆ
) +
b d
(ˆ
·
ˆ
)
=
a c
+
b d .
005
10.0 points
A little boy is running along the aisle of a train
moving at constant velocity. A man standing
at a station sees the train go by and through
its windows measures the velocity of the little
boy as
vectorv
b
. The passengers on the train, sitting
quietly in their seats, measure the velocity of
the little boy as
vectorv
t
.
What is the velocity of the train itself with
respect to the station;
i.e.
, the ground?
1.
vectorv
t

vectorv
b
2.
vectorv
b

vectorv
t
correct
3.
vectorv
t
+
vectorv
b
4.
zero
Explanation:
vectorv
bt
+
vectorv
ts
=
vectorv
bs
vectorv
ts
=
vectorv
bs

vectorv
bt
=
vectorv
b

vectorv
t
.
006
10.0 points
Let
A
=
i
,
B
=
i
+
j
and
C
=
j
.
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 Spring '11
 Zao
 Physics, Acceleration, Velocity, Huynh

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