homework 04 – FRENNEA, KYLE – Due: Feb 13 2007, 4:00 am
1
Question 1
part 1 of 1
10 points
A boat moves through the water of a river
at 14
.
5 m
/
s relative to the water, regardless
of the boat’s direction.
If the current is flowing at 12
.
3 m
/
s, how
long does it take the boat to complete a trip
consisting of a 268 m displacement down
stream followed by a 196 m displacement up
stream?
Correct answer: 99
.
0909 s (tolerance
±
1 %).
Explanation:
Let
v
b
be the velocity of the boat relative
to the water, and
v
w
the velocity of water
relative to the shore. Take downstream as the
positive direction.
For the downstream trip,
the current is speeding him up, so the velocity
of the boat relative to the shore is
v
d
=
v
b
+
v
w
and the time is
t
d
=
x
d
v
d
=
x
d
v
b
+
v
w
For the upstream trip, the current is slowing
him down, so the velocity of the boat relative
to the shore is
v
u
=
v
b
−
v
w
and the time is
t
u
=
x
u
v
u
=
x
u
v
b
−
v
w
The time for the entire trip is thus
t
=
t
d
+
t
u
=
x
d
v
b
+
v
w
+
x
u
v
b
−
v
w
=
(268 m)
(14
.
5 m
/
s) + (12
.
3 m
/
s)
+
(196 m)
(14
.
5 m
/
s)
−
(12
.
3 m
/
s)
=
99
.
0909 s
Question 2
part 1 of 1
10 points
A flashbulb is placed in the middle of a
bus. When the flashbulb goes off, light from
the bulb strikes the rear and front of the bus
simultaneously, as seen by an observer, Karl,
sitting in the bus.
As seen by another observer, Fred, standing
on the curb as the bus moves past, the light
.
1.
hits the front of the bus slightly before it
hits the rear.
2.
hits the front and back of the bus simul
taneously.
3.
Not enough information to form a conclu
sion.
4.
hits the rear of the bus slightly before it
hits the front.
correct
Explanation:
Both Karl and Fred observe the radiation
moving at the same speed, but in Fred’s frame
of reference, the rear of the bus moves to
ward the spot where the radiation was emitted
while the front moves away, so the radiation
reaches the rear of the bus first.
Question 3
part 1 of 2
10 points
A cheetah can run at a maximum speed
98
.
1 km
/
h and a gazelle can run at a maxi
mum speed of 71
.
1 km
/
h.
If both animals are running at full speed,
with the gazelle 66
.
4 m ahead, how long before
the cheetah catches its prey?
Correct answer: 8
.
85333 s (tolerance
±
1 %).
Explanation:
The relative velocity of the cheetah with re
spect to gazelle:
Δ
v
=
v
ch
−
v
ga
= 98
.
1 km
/
h
−
71
.
1 km
/
h
= 27 km
/
h
= 27 km
/
h
×
1000 m
/
km
3600 s
/
h
= 7
.
5 m
/
s
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homework 04 – FRENNEA, KYLE – Due: Feb 13 2007, 4:00 am
2
The relative distance which the cheetah has
to cover is Δ
x
= 66
.
4 m.
Then the time it
takes the cheetah to catch the gazelle is :
t
=
Δ
x
Δ
v
=
66
.
4 m
7
.
5 m
/
s
= 8
.
85333 s
Question 4
part 2 of 2
10 points
The cheetah can maintain its maximum
speed for only 7
.
5 s.
What is the minimum distance the gazelle
must be ahead of the cheetah to have a chance
of escape? (After 7
.
5 s the speed of cheetah is
less than that of the gazelle)
Correct answer: 56
.
25 m (tolerance
±
1 %).
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 Spring '08
 Turner
 Current, Force, Work, Correct Answer, KYLE

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