Chapter 1
Part 1 of 2
Example Problems & Solutions
(useful for homework)
1
1
• 1
1. The largest diamond ever found had a
size of 3106 carots. One carot is
equivalent to a mass of 0
0.200
200 g
g. Use the
fact that 1 kg (1000 g) has a weight of
2 205 lb under certain conditions
2.205
conditions, and
determine the weight of this diamond in
pounds.
pounds
2
3
5
• 5
5. The mass of the parasitic wasp can be
as small as 5x10-6 kg. What is this mass in
(a) grams,
grams (b) milligrams,
milligrams (c) micrograms.
micrograms
4
5
9
9. The depth of the ocean is sometimes measured in
fathoms (1 fathom = 6 feet). Distance on the surface of the
ocean is sometimes measured in nautical miles (1 nautical
mile = 6076 feet). The water beneath a surface rectangle
1.20 nautical miles by 2.60 nautical miles has a depth of
16 0 fathoms
16.0
fathoms. Find the volume
ol me of water
ater (in ccubic
bic meters)
beneath this rectangle.
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7
13
• 13
13. A highway is to be built between two
towns, one of which lies 35.0 km south
and 72
72.0
0 km west of the other
other. What is the
shortest length of highway that can be built
between the two towns
towns, and what angle
would this highway be directed with
respect to due west ?
8
9
19
• 19. Three deer, A, B,C are grazing in a field. Deer B is
located 62 m from deer A at an angle of 51 degrees
north of west. Deer C is located 77 degrees north of
east relative to deer A. The distance between deer B
and C is 95 m. What is the distance between deer A
and
d C ? (Hint:
(Hi t consider
id the
th llaw off cosines
i
given
i
below)
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11
23
• 23
23. A circus performer begins his act by
walking out along a nearly horizontal high
wire He slips and falls to the safety net
wire.
net,
25.0 ft below. The magnitude of his
displacement from thebeginning of the
walk to the net is 26.7 ft. (a) How far out
along the high wire did he walk ? (b) Find
the angle that his displacement vector
makes below the horizontal
horizontal.
12
13
25
25. One displacement
p
vector A has a magnitude
g
of
2.43 km and points due north.
A second displacement vector B has a magnitude of
7.74 km and also points due north.
(a) Find the magnitude and direction of A
A-B.
B
(b) Find the magnitude and direction of B-A.
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15
27
27. A car is being pulled out of the mud by two forces that are applied by the
t
two
ropes shown
h
in
i th
the drawing
d
i
The dashed line in the drawing bisects the 30.0 degree angle.
The magnitude of the force applied by each rope is 2900 Newtons.
Arrange the force vectors tail to head and use the graphical technique to
answer the following questions.
(a) How much force would a single rope need to apply to accomplish the same
effect as the two forces added together ?
(b) How would the single rope be directed relative to the dashed line ?
2900 N
o
30
car
2900 N
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17
31
• 31
31. Vector A points along the +y axis and
has a magnitude of 100.0 units. Vector B
points at an angle of 60
60.0
0 degrees above
the +x axis and has a magnitude of 200.0
units Vector C points along the +x axis
units.
and has a magnitude of 150.0 units. Which
vector has the largest x component and
(b) the largest y component?
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19