Patel (pnp223) – homework 13 – Turner – (92160)
1
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printout
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have
9
questions.
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before answering.
001
10.0 points
A hunter wishes to cross a river that is 1
.
7 km
wide and that flows with a speed of 6
.
2 km
/
h.
The hunter uses a small powerboat that moves
at a maximum speed of 12 km
/
h with respect
to the water.
What is the time necessary for crossing
if the boat moves directly across the river?
Draw the vectors to scale on a graph to deter
mine the answer.
Correct answer: 9
.
92774 min.
Explanation:
Let :
Δ
x
= 1
.
7 km
,
v
re
= 6
.
2 km
/
h
,
and
v
br
= 12 km
/
h
.
v
be
6
.
2 km
/
h
12 km
/
h
Scale: 10 km
/
hr
We need to find the angle to head
into
the current so that the resultant direction is
perpendicular to the current
v
br
sin
θ
=
v
re
sin
θ
=
v
re
v
br
θ
= sin
−
1
parenleftbigg
v
re
v
br
parenrightbigg
= sin
−
1
parenleftbigg
6
.
2 km
/
h
12 km
/
h
parenrightbigg
= 31
.
1089
◦
.
Thus
v
be
=
v
br
cos
θ
= (12 km
/
h) cos(31
.
1089
◦
)
= 10
.
2742 km
/
h
.
and
Δ
t
min
=
Δ
x
v
be
=
Δ
x
v
br
cos
θ
=
1
.
7 km
(12 km
/
h) cos(31
.
1089
◦
)
60 min
1 h
=
9
.
92774 min
.
Alternate Solution:
v
be
=
radicalBig
v
2
be

v
2
re
Δ
t
min
=
Δ
x
v
be
=
(1
.
7 km)
radicalbig
(10
.
2742 km
/
h)
2

(6
.
2 km
/
h)
2
=
(1
.
7 km)
(10
.
2742 km
/
h)
60 min
1 h
=
9
.
92774 min
.
002
10.0 points
A car is moving at constant speed on the
freeway. The driver sees a patrol car at time
t
1
and rapidly slows down by around 10 miles
per hour. After continuing at this speed for a
few minutes, the driver at time
t
2
returns to
the earlier constant speed.
Let us plot the
acceleration
of the car as a
function of time; take the forward direction
of motion as positive. Which graph correctly
describes the car’s acceleration
a
(
t
)?
1.
t
1
time
0
0
a
t
2
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Patel (pnp223) – homework 13 – Turner – (92160)
2
2.
t
1
time
0
0
a
t
2
3.
t
1
time
0
0
a
t
2
correct
4.
t
1
time
0
0
a
t
2
5.
t
1
time
0
0
a
t
2
6.
t
1
time
0
0
a
t
2
7.
t
1
time
0
0
a
t
2
8.
t
1
time
0
0
a
t
2
Explanation:
The car is at first moving at a constant
speed and therefore its acceleration is zero.
After seeing a patrol car it starts slowing
down;
i.e.
, decelerating for a short while. Dur
ing that time period its acceleration is nega
tive. The acceleration soon goes back to zero
and stays at zero while the car moves at a
constant (but lower) speed once again.
At
time
t
2
the car briefly accelerates (so its ac
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 Spring '09
 Turner
 Physics, Acceleration, Work, Velocity, m/s, patel, Miles per hour

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