Physics 112  HW #2 Solutions
Spring 2006
147
[Vector Components]
(d)
(a)

A
→
=
(4.00)
2
+ (3.00)
2
= 5.00

B
→
=
(5.00)
2
+ (2.00)
2
= 5.39
(b)
A
→

B
→
= 1.00
i
∧
+ 5.00
j
∧
(c)

A
→

B
→
=
(1.00)
2
+ (5.00)
2
= 5.10
151
[Dot Product & Angles]
(a)
A
→
•
B
→
=(4.00
×
5.00+3.00
×
(2.00))=14.0
(b)
A
→
•
B
→
=
A
→

B
→
cos(
θ
)
⇒
cos
θ
=
A
→
•
B
→

A
→

B
→

=
14.0
(5.00) (5.39)
=
0.519
⇒
θ
=
59°
 1 
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1.66 [Vector Addition]
(
)
(
)
344
.
0
km
311.5
km
2
.
107
tan
km
330
km
2
.
107
km
5
.
311
km
2
.
107
48
sin
km)
230
(
68
cos
km)
170
(
km
5
.
311
48
cos
km)
230
(
68
sin
km)
170
(
2
2
2
2
=
=
=
=
−
+
=
+
=
−
=
−
=
+
=
=
+
=
+
=
x
y
R
y
x
y
y
y
x
x
x
R
R
θ
R
R
R
B
A
R
B
A
R
D
D
D
D
east
of
south
19
D
=
R
θ
2.19
[Motion Diagrams]
 2 
b)
2.35:
a)
b) From the graph (Fig. (2.35)), the curves for
A
and
B
intersect at
t
= 1 s and
t
= 3 s.
c)
d) From Fig. (2.35), the graphs have the same slope at
t
= 2 s .
e) Car
A
passes car
B
when they
have the same position and the slope of curve
A
is greater than that of
curve
B
in Fig. (2.30);
this
is at
t
= 3 s.
f) Car
B
passes car
A
when they have the same position and the slope of curve
B
is
greater than that of curve
A
; this is at
t
= 1 s.
 3 
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