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Chapter 2 Problems
2.58
A rock is thrown vertically uward from ground level at time t=0.
At t=1.5s, it passes the to
of a tall tower and 1.0 s later, it reaches its maximum height.
What is the height of the tower
t=1.5s
t=2.5s
t=0 s
y
1.5
=h
y
2.5
We begin by considering the t=0 to t=1.5s part of the trip.
y
i
= 0
m
y
1.5
=
h
v
i
= ?
v
1.5
= ?
a
=
g
t
= 1.5
s
We can Fnd the height if we have the initial velocity, using
y
1.5
=
y
i
+
v
i
t
+
2
1
a t
2
To Fnd the initial velocity, we consider the entire 2.5 second trip.
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View Full Document y
i
= 0
m
y
2.5
= ?
v
i
= ?
v
2.5
= 0
a
=
g
t
= 2.5
s
v
2.5
=
v
i

g
$
2.5
s
v
i
=
g
$
2.5
s
= 24.5
m
/
s
Now that we know the initial velocity, we can fnd the height oF the tower.
y
1.5
=
y
i
+
v
i
t
+
2
1
a t
2
y
1.5
=
y
i
+ 24.5
m
/
s
$
1.5
s

2
1
$
9.8
m
/
s
2
$
(1.5
s
)
2
= 25.725
m
2.67
How Far does the runner whose velocitytime graph is shown in ±ig 2036 travel in 16 s?
The fgure’s vertical scaling is et by v
s
=8.0m/s
The runner’s displacement is the area under the curve.
We can compute the area geometrically
A
=
2
1
$
2
s
$
8
m
/
s
+ 8
s
$
8
m
/
s
+
2
1
$
2
s
$
4
m
/
s
+ 2
s
$
4
m
/
s
+ 4
s
$
4
m
/
s
= 100
m
2.108
A ball is thrown vertically downward From the top oF a 36.6m tall building.
The ball
passes the top oF a window that is 12.2m above the ground 2.00s aFter being thrown.
What is
the speed oF the ball as it passes the top oF the window?
t=0s
t=2.0 s
y
i
=36.6m
y
f
=12.2m
Once again, we write what we know
y
i
= 36.6
m
y
f
= 12.2
m
v
i
= ?
v
f
= ?
a
=
g
t
= 2.0
s
As in the previous problem, we need the initial velocity to fnd the result that we are looking For
in this case the fnal velocity.
We can fnd the initial velocity
y
f
=
y
i
+
v
i
t
+
2
1
a t
2
=
y
i
+
v
i
t

2
1
g t
2
v
i
=
t
y
f

y
i
+
2
1
g t
2
=2.4
m
/
s
We can now fnd the fnal velocity
v
f
=
v
i
+
at
m
/
s
 9.8
m
/
s
2
$
2
s
=22
m
/
s
Chapter 3 Problems
3.1
The x component oF a certain vector is 25.0 units and the y component is +40 units.
(a)
What is the magnitude and direction oF the vector?
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This note was uploaded on 09/27/2010 for the course ASD 2456 taught by Professor Jojo during the Spring '10 term at Brooklyn Law School.
 Spring '10
 jojo

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