Chapter 1
Part 1 of 2
Example Problems & Solutions
(useful for homework)
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• 1. The largest diamond ever found had a
size of 3106 carots. One carot is
equivalent to a mass of 0.200 g. Use the
fact that 1 kg (1000 g) has a weight of
2.205 lb under certain conditions, and
determine the weight of this diamond in
pounds.
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5
• 5. The mass of the parasitic wasp can be
as small as 5x10-6 kg. What is this mass in
(a) grams, (b) milligrams, (c) micrograms.
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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. Find the
volume of water (in cubic meters) beneath this rectangle.
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13
• 13. A highway is to be built between two
towns, one of which lies 35.0 km south
and 72.0 km west of the other. What is the
shortest length of highway that can be built
between the two towns, and what angle
would this highway be directed with
respect to due west ?
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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
releative to deer A. The distance between
deer B and C is 95 m. What is the distance
between deer A and C ? (Hint: consider
the law of cosines given in Appendix E)
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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,
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.
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25
25. One displacement vector A has a magnitude 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-B.
(b) Find the magnitude and direction of B-A.
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27
• 27. A car is being pulled out of the mud by two forces
that are applied by the two ropes shown in the drawing
(page 23, problem 27 of your text).
• 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 techniqu eto 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 ?
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31
• 31. Vector A points along the +y axis and
has a magnitude of 100.0 units. Vector B
points at an angle of 60.0 degrees above
the +x axis and has a magnitude of 200.0
units. Vector C points along the +x axis
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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