roofner (bar784) – Homework 17 – Weathers – (17104)
1
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printout
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have
10
questions.
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before answering.
001
(part 1 of 2) 10.0 points
a) Find the time it takes an object to hit the
ground when it is dropped from a height of 66
using the model
h
=

16
t
2
+
s,
where
s
is the initial height, and
t
is in sec
onds.
Correct answer: 2
.
03101 sec.
Explanation:
h
=

16
t
2
+ 66
The ball hits the ground at
h
= 0, so
0 =

16
t
2
+ 66
16
t
2
=
+ 66
16
t
2
16
=
66
16
t
2
= 4
.
125
√
t
2
=
±
√
4
.
125
t
≈ ±
2
.
03101
Time must be positive, so
t
≈
2
.
03101 sec
.
002
(part 2 of 2) 10.0 points
b) Find the time it takes an object to hit the
ground when it is dropped from a height of
132 ft.
Correct answer: 2
.
87228.
Explanation:
h
=

16
t
2
+ 132
The ball hits the ground at
h
= 0. Thus the
time of fall can be found from
0 =

16
t
2
+ 132
16
t
2
=
+ 132
16
t
2
16
=
132
16
t
2
= 8
.
25
√
t
2
=
±
√
8
.
25
t
≈ ±
2
.
87228
t
cannot be negative, so
t
≈
2
.
87228
.
Note that doubling the distance does not dou
ble the time.
003
(part 1 of 2) 10.0 points
Given:
G
= 6
.
67259
×
10

11
N m
2
/
kg
2
Two hypothetical planets of masses 3
.
2
×
10
23
kg and 6
.
1
×
10
23
kg and radii 3
.
9
×
10
6
m
and 7
.
8
×
10
6
m, respectively, are at rest when
they are an infinite distance apart.
Because
of their gravitational attraction, they head
toward each other on a collision course.
When their centertocenter separation is
7
.
4
×
10
8
m, find their relative velocity.
Correct answer: 408
.
967 m
/
s.
Explanation:
At infinite separation the potential energy
U
is zero, and at rest the kinetic energy
K
is
zero. Since energy is conserved we have
0 =
1
2
m
1
v
2
1
+
1
2
m
2
v
2
2

G m
1
m
2
d
.
The initial momentum is zero and momentum
is conserved, so
0 =
m
1
v
1

m
2
v
2
.
Combine these two equations to find
v
1
=
m
2
radicalBigg
2
G
d
(
m
1
+
m
2
)
= 6
.
1
×
10
23
kg
×
radicalBigg
2 (6
.
67259
×
10

11
N m
2
/
kg
2
)
(7
.
4
×
10
8
m) (9
.
3
×
10
23
kg)
= 268
.
247 m
/
s
v
2
=
m
1
radicalBigg
2
G
d
(
m
1
+
m
2
)
= 3
.
2
×
10
23
kg
×
radicalBigg
2 (6
.
67259
×
10

11
N m
2
/
kg
2
)
(7
.
4
×
10
8
m) (9
.
3
×
10
23
kg)
= 140
.
72 m
/
s
.
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