Homework 1 Due January 16 2007
1)
Suppose that
B
A
C
G
G
G
+
=
and
B
A
D
G
G
G
−
=
a.
In general, show that
B
A
C
+
≤
with a geometric argument.
b.
Write an expression for
B
A
G
G
⋅
in terms of
A, B and C.
c.
Write an expression for
B
A
G
G
⋅
in terms of
2
C
and
2
D
.
d.
If
B
A
C
−
=
, what must be true about the relative orientation of these
three vectors? Draw a sketch to illustrate your answer
. In this case what is
D (i.e. the magnitude of
D
G
)?
e.
If C=A+B, what must be true about the relative orientation of these three
vectors? Draw a sketch to illustrate your answer
.
2)
Consider the vectors shown in Figure 11. Plot them out on graph paper:
a.
Graphically determine the magnitude and direction of:
Q
P
G
G
+
b.
Graphically determine the magnitude and direction of:
Q
P
G
G
−
c.
Determine the
value of
Q
P
G
G
⋅
.
3)
If John walks east 3km at a speed of 4km/hr and then runs west at a speed of
12km/hr for 2hr, what is his average velocity?
4)
A car is initially traveling at a speed of 30km/hr. After it accelerates at a constant
rate and travels a distance of 20km down the road, it is moving at a speed of
50km/hr.
a.
What is the acceleration of the car?
b.
How long does it take to cover the 20km?
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 Spring '08
 HerreraSiklody
 Acceleration, Work, Velocity, 2 km, 7m/s, 0.5m, 14°

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