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001
10.0 points
A flowerpot is knocked off a balcony 25
.
5 m
above the sidewalk and falls toward an un
suspecting 1
.
64 m tall man who is standing
below.
How close to the side walk can the flower
pot fall before it is too late for a warning
shouted from the balcony to reach the man in
time?
Assume that the man below requires
0
.
249 s to respond to the warning, and the
velocity of sound in air to be 344 m
/
s.
The
acceleration of gravity is 9
.
8 m
/
s
2
.
Correct answer: 8
.
02803 m.
Explanation:
Let :
v
s
= 344 m
/
s
,
H
= 25
.
5 m
,
h
m
= 1
.
64 m
,
and
t
r
= 0
.
249 s
.
h
2
=
gt
2
2
/2
t
2
=
t

t
1
h
=
H

h
m
t
= (2
h
/
g
)
1/2
h
1
=
h

h
2
t
1
=
t
r
+
t
s
h
m
h
m
H
H
1
The distance from the balcony to the man’s
head is
h
=
H
−
h
m
,
The time for a warning to travel this dis
tance is
t
s
=
h
v
s
=
H
−
h
m
v
s
.
The total time needed to receive the warn
ing and react is
t
1
=
t
s
+
t
r
=
H
−
h
m
v
s
+
t
r
,
and the time for the pot to fall this distance
(starting from rest) is
t
=
radicalBigg
2
h
g
=
radicalBigg
2 (
H
−
h
m
)
g
.
Thus the latest the warning can be sent is
at
t
2
=
t
−
t
1
=
radicalBigg
2 (
H
−
h
m
)
g
−
H
−
h
m
v
s
−
t
r
=
radicalBigg
2 (25
.
5 m
−
1
.
64 m)
9
.
8 m
/
s
2
−
25
.
5 m
−
1
.
64 m
344 m
/
s
−
0
.
249 s
= 1
.
88831 s
into the fall. In this time the pot has fallen a
distance of
h
2
=
1
2
g t
2
2
and the corresponding height above the side
walk is
H
1
=
H
−
h
2
=
H
−
1
2
g t
2
2
= 25
.
5 m
−
1
2
(
9
.
8 m
/
s
2
)
(1
.
88831 s)
2
=
8
.
02803 m
.
002
10.0 points
Sound waves travel through a liquid of density
9240 kg
/
m
3
at a speed of 4440 m
/
s.
What is the bulk modulus of this liquid?
Correct answer: 1
.
82154
×
10
11
Pa.
Explanation:
Let :
ρ
= 9240 kg
/
m
3
and
v
sound
= 4440 m
/
s
.
homework 39 – Turner – (58185)
1
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hinojosa (jlh3938) – homework 39 – Turner – (58185)
2
In fluids, sound waves are pressure waves,
and their speed depends on the fluid’s density
and bulk modulus:
v
sound
=
radicalBigg
B
ρ
.
For the liquid in question, we know the
density and the speed of sound, so the bulk
modulus is
B
=
ρ v
2
sound
= (9240 kg
/
m
3
) (4440 m
/
s)
2
=
1
.
82154
×
10
11
Pa
.
003
10.0 points
A harmonic wave
y
=
A
sin[
k x
−
ω t
−
φ
]
,
where
A
= 1 m,
k
has units of m
−
1
,
ω
has
units of s
−
1
, and
φ
has units of radians, is
plotted in the diagram below.
+1
−
1
A
(meters)
t
(seconds)
10
20
30
At the position
x
= 0
Which wave function corresponds best to
the diagram?
1.
y
=
A
sin
bracketleftbigg
k x
−
parenleftbigg
2
π
15 s
parenrightbigg
t
−
parenleftbigg
2
π
3
parenrightbiggbracketrightbigg
2.
y
=
A
sin
bracketleftbigg
k x
−
parenleftbigg
2
π
15 s
parenrightbigg
t
−
parenleftbigg
1
π
3
parenrightbiggbracketrightbigg
3.
y
=
A
sin
bracketleftbigg
k x
−
parenleftbigg
2
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 Spring '08
 Turner
 Work, Correct Answer, Hinojosa

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