Version 010 – exam1 – bohm – (59970)
1
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11
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001
10.0 points
You and your friend throw balloons filled with
water from the roof of a several story apart
ment house. You simply drop a balloon from
rest.
A second balloon is thrown downward
by your friend 3
.
3 s later with an initial speed
of 64
.
68 m
/
s. They hit the ground simultane
ously.
The acceleration of gravity is 9
.
8 m
/
s
2
.
You
can neglect air resistance.
How high is the apartment house?
1. 68.9062
2. 159.201
3. 167.69
4. 53.361
5. 127.449
6. 80.3723
7. 44.1
8. 74.529
9. 142.884
10. 120.062
Correct answer: 120
.
062 m.
Explanation:
For balloon 1:
y
1
=
1
2
g t
2
1
For balloon 2:
y
2
=
v
0
t
2
+
g t
2
2
2
Balloon 2 is thrown Δ
t
seconds after balloon
1 and they hit the ground at the same time,
so:
t
1
=
t
2
+ Δ
t
Since the height of the house is the same for
both of the balloons,
y
1
=
y
2
g t
2
1
2
=
v
0
(
t
1

Δ
t
) +
g
2
(
t
1

Δ
t
)
2
(
v
0

g
Δ
t
)
t
1
=
v
0
Δ
t

g
2
Δ
t
2
t
1
=
v
0
Δ
t

g
2
Δ
t
2
v
0

g
Δ
t
=
Δ
t
2
+
v
0
v
0

g
Δ
t
Δ
t
2
For Δ
t
= 2 s
t
1
= 1 +
v
0
v
0

2
g
For
v
0
= 30 m/s, Δ
t
= 2 s
t
1
= 4
.
95 s
From the above, once
t
1
is known, the height
of the house is given simply by
y
=
g t
2
1
2
For
t
1
= 4
.
95 s,
y
= 120
.
062 m
002
10.0 points
Three vectors
vector
A
,
vector
B
, and
vector
C
have the following
x
and
y
components:
A
x
= 7
.
9,
A
y
=

6
.
3;
B
x
=

3
.
8,
B
y
= 4
.
5;
C
x
= 2
.
7,
C
y
= 5
.
7.
What is the magnitude of
vector
A
+
vector
B
+
vector
C
?
1. 8.5235
2. 8.27345
3. 2.33452
4. 3.80132
5. 9.45569
6. 7.83901
7. 2.06155
8. 3.67967
9. 10.5385
10. 5.59017
Correct answer: 7
.
83901.
Explanation:
Given :
vector
A
= (7
.
9
,

6
.
3)
,
vector
B
= (

3
.
8
,
4
.
5)
,
and
vector
C
= (2
.
7
,
5
.
7)
.
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Version 010 – exam1 – bohm – (59970)
2
Let
vector
D
=
vector
A
+
vector
B
+
vector
C
. The
x
component o f
vector
D
is
D
x
=
A
x
+
B
x
+
C
x
= 7
.
9+(

3
.
8)+2
.
7 = 6
.
8
and the
y
component of
vector
D
is
D
y
=
A
y
+
B
y
+
C
y
=

6
.
3 + 4
.
5 + 5
.
7 = 3
.
9
.
Thus the magnitude of
vector
A
+
vector
B
+
vector
C
is given by
D
=
radicalBig
D
2
x
+
D
2
y
=
radicalbig
6
.
8
2
+ 3
.
9
2
=
7
.
83901
.
003
10.0 points
A car travels along a straight stretch of road.
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 Spring '08
 Kaplunovsky
 Acceleration, Velocity, Correct Answer, 7 kg, 13 mi, 3.4 m

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