Ch
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Homework
Name:
Follow the instructions on the problems and show your work clearly.
1. (Problem 3)
A shape that covers an area A and has a uniform height h has a volume V = Ah.
(a) Draw a cylinder and a rectangular
box that cover an area A and height h.
i
t
tL
I,L
b
L
(b)
Show that V = Ah is dimensionally correct.
v) = '7n3
IA A1 2 t/+l LLJ
L
=
=
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4a'fh
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re [vf = tA L1 : ?^3
)
V
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olisn>;onol! corrPcL
(c) Show that the volumes of a cylinder and of a rectangular box can be written
in the form Y =Ah,
identifying A in each case.
(Note the A, sometimes called the "footprint" of the object, can have any shape and that the
e
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height can, in general, be replaced bythe average thickness of the object)
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of ,\ cTlintbr =
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fr vtn ol '*'tn^Vle : ^b=A
Vrlu^g
o- recton6,ttlar box = AL=
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2. (Problem 11)
A block of gold has length 6.23 cm, width 5.35 cm and height 3.02 cm.
(a) Calculate the length time the width and round the answer to the appropriate number of
significant figures.
6 ,L3r* x 5 ,35cn:
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hi{
0
1
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(b) Now multiply the rounded result of part
(a) by the height and again round, obtaining the volume
(write down units).
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2 r*t
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(c)
#
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Repeat the process, first findlng the width times the height, rounding it and then obtaining the
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volume by multiplying by the length.
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(d)
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=
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lo
Read section 1.4 and Explain why the answers don't agree in the third significant figure.
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3. (Problem 25)
The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers an
area of one acre to a depth of one foot. An acre is 43,560 ft2 . Find the volume in Sl units of a reservoir
containing 25.0 acre-ft of water.
(a) Convert 25.0 acre-ft to
ft3.
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llD^4
l,o z gooo
=
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#
(b) Convert ft' to m3.lconversion factor is on the front cover of the text book)
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2 ,33> r tiTttt3
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4.(Problem 29)
Estimate the number of breaths taken by a human being during an average life time.
(a) Estimate the number of breath take
R, "6A
(b) Estimate
l7
L
by a human being during a minute.
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brp*th
s
Fer
7,^ i
v
,i(. L'
/ ,c bre,.+atA;n
an average life time of a human
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ly SOye"rs ^-
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>+lrs
6o
(c) Convert the life time to minutes
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sJYs
I y"nf
(d) Estimate the number of breaths taken
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lF
/ -I d^f
un
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1\-
by a human being during an average life time.
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2 ,560
rCIoa
*in
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rr
/ l;t't tiue
.
5.(Problem 38)
Two points in a rectangular coordinate system have the coordinates (2.0, 3.0) and (-2.0, 1.0), where the
units are centimeters. Determine the distance between these points.
(a) Draw the two points on the rectangular coordinate system below.
L
2
Ll
-2
0
2
-2
(b) Determine the distance between these points.
Vsiry
PYtA^ftorean -rkt*rrms
d-W
= lt,
tru
=L$
I
6.(Problem 41)
For the triangle shown in Figure below, what are (a) the length of the unknown side, (b) the tangent of 0,
and (c) the sine of $?
6.00 m
(a)
Using Pythagorean theorem, find the length of the unknown side
= 3,8=
(b) Calculate tan0
t^nB= $,00u
6,11 ^
(c) Calculate sin$
|in (
(d) (extra problem)What
=
.6 ,!tr_
Q,otsu
=lo,qnl)
are the angle $ and 0? ( You can use inverse sine or inverse tangent
function in a calculator)
-l
\a-
=l +8,7'
P
=l+1.8'
7
7.(Problem 49)_
A surveyor measures the distance across a straight river by the following method: Starting directly
across from a tree on the opposite bank, he walks x = 100 m along the riverbankto establish a baseline.
Then he sights across to the tree. The angle from his baseline to the tree is 0 = 35'(See Figure below).
How wide is the river?
(a) Write y in terms of x and 0. (Use symbols. Do not use numbers)
)=
(b)
)C{srh 0
Using the numbers in the problem(x = 100 m, 0 = 35o), calculate the yvalue.
Y=
lraa f"n 3-f "
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