homework 01 – ASH, BEN – Due: Jan 30 2008, 11:00 pm
1
Question 1, chap 1, sect 1.
part 1 of 2
10 points
Two points in the
xy
plane have cartesian
coordinates (
x
1
, y
1
) and (
x
2
, y
2
), where
x
1
=
8
.
6 m,
y
1
=
−
10 m,
x
2
=
−
10 m, and
y
2
=
4 m.
Determine
the
distance
between
these
points.
Correct answer: 23
.
28 m (tolerance
±
1 %).
Explanation:
By simple geometry of triangle, the dis
tance between two points is
d
=
radicalBig
[
x
2
−
x
1
]
2
+ [
y
2
−
y
1
]
2
=
braceleftbigg
bracketleftBig
(
−
10 m)
−
(8
.
6 m)
bracketrightBig
2
+
bracketleftBig
(4 m)
−
(
−
10 m)
bracketrightBig
2
bracerightbigg
1
2
= 23
.
28 m
.
Question 2, chap 1, sect 1.
part 2 of 2
10 points
What is the angle between the line con
necting the two points and
x
axis (measured
counterclockwise, within the limits of
−
180
◦
to +180
◦
)?
Correct answer: 143
.
032
◦
(tolerance
±
1 %).
Explanation:
The angle between the line connecting the
two points and
x
axis (positive in counter
clockwise direction) is
θ
= arctan
bracketleftbigg
y
2
−
y
1
x
2
−
x
1
bracketrightbigg
= arctan
bracketleftbigg
(4 m)
−
(
−
10 m)
(
−
10 m)
−
(8
.
6 m)
bracketrightbigg
= arctan
bracketleftbigg
(14 m)
(
−
18
.
6 m)
bracketrightbigg
= 2
.
49637 rad
= 143
.
032 deg
.
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
(
−
10, 4)
(8
.
6,
−
10)
143
.
032 deg
Question 3, chap 1, sect 2.
part 1 of 1
10 points
The standard of time is based on
1.
the yearly revolution of the earth about
the sun.
2.
the daily rotation of the earth.
3.
the frequency of light emitted by
86
Kr.
4.
None of these
correct
5.
a precision pendulum clock.
Explanation:
The second is defined from oscillations of
cesium133 atoms.
Question 4, chap 1, sect 4.
part 1 of 1
10 points
A spherical balloon with radius
r
inches has
volume
V
=
4
3
π r
3
.
Find a function that represents the amount
of air required to inflate the balloon from a
radius of
r
inches to a radius of
r
+ 1 inches.
1.
4
3
π
(
3
r
+ 1
r
2
+ 1
)
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homework 01 – ASH, BEN – Due: Jan 30 2008, 11:00 pm
2
2.
4
3
π
(
r
+ 1)
3
3.
4
3
π
(
3
r
+ 3
r
2
+ 1
)
correct
4.
4
3
π
(
1
r
+ 3
r
2
+ 1
)
5.
4
3
π r
3
Explanation:
Δ
V
=
4
3
π
(
r
+ 1)
3
−
4
3
π r
3
=
4
3
π
(
r
3
+ 3
r
+ 3
r
2
+ 1
−
r
3
)
=
4
3
π
(
3
r
+ 3
r
2
+ 1
)
.
Question 5, chap 1, sect 5.
part 1 of 1
10 points
In one scene in the movie
The Godfather II
,
a solid gold phones is passed around a large
table for everyone to see. Suppose the volume
of gold in the phone was equal to the volume
of 10centimeter cube of gold (the density of
gold is 19,300 kg/m
3
).
Do you think such a phone could be causu
ally passed around a table from hand to hand?
What is the weight of the phone?
1.
No. It weighs about 45 lbs.
correct
2.
Yes. It weighs about 9 lbs.
3.
No. It weighs about 90 lbs.
4.
Yes. It weighs about 4.5 lbs.
Explanation:
One cubic meter of gold has a mass of about
20,000 kg, which is roughly 45,000 pounds.
A ten centimeter cube of gold is about 45
pounds. It would be difficult to pass around
this phone.
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 Spring '08
 ERSKINE/TSOI
 Acceleration, Work, Velocity, Correct Answer

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