homework 03 – JACOBS, AMBER – Due: Feb 5 2008, 1:00 am
1
Question 1, chap 4, sect 5.
part 1 of 1
10 points
A toy cannon fires a 0
.
1 kg shell with initial
velocity
v
i
= 9
.
7 m
/
s in the direction
θ
= 47
◦
above the horizontal.
The acceleration of gravity is 9
.
8 m
/
s
2
.
Δ
x
Δ
h
9
.
7 m
/
s
47
◦
Δ
y
y
Shell’s trajectory curves downward because
of gravity, so at the time
t
= 0
.
782 s the shell
is below the straight line by some vertical
distance.
Your task is to calculate this distance Δ
h
in the absence of air resistance.
Correct answer:
2
.
99647
m (tolerance
±
1
%).
Explanation:
In the absence of gravity, the shell would fly
along the straight line at constant velocity:
ˆ
x
=
t v
i
cos
θ ,
ˆ
y
=
t v
i
sin
θ .
The gravity does not affect the
x
coordinate
of the shell, but it does pull its
y
coordinate
at constant downward acceleration
a
y
=
−
g
,
hence
x
=
t v
i
cos
θ,
y
=
t v
i
sin
θ
−
g t
2
2
.
Thus,
x
= ˆ
x
but
y
= ˆ
y
−
1
2
gt
2
, or in other
words, the shell deviates from the straightline
path by the vertical distance
Δ
h
=

ˆ
y
−
y

=
g t
2
2
.
Note:
This result is completely indepen
dent on the initial velocity
v
i
or angle
θ
of
the shell. It is a simple function of the flight
time
t
and nothing else (besides the constant
g
= 9
.
8 m
/
s
2
).
Δ
h
=
g t
2
2
=
(9
.
8 m
/
s
2
) (0
.
782 s)
2
2
=
2
.
99647 m
.
Question 2, chap 4, sect 5.
part 1 of 1
10 points
A ball is thrown and follows the parabolic
path shown. Air friction is negligible. Point
Q
is the highest point on the path. Points
P
and
R
are the same height above the ground.
Q
R
P
Which of the following diagrams best indi
cates the direction of the acceleration, if any,
on the ball at point
R
?
1.
The ball is in freefall and there is no
acceleration at any point on its path.
2.
correct
3.
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homework 03 – JACOBS, AMBER – Due: Feb 5 2008, 1:00 am
2
4.
5.
6.
7.
8.
9.
Explanation:
Since air friction is negligible, the only ac
celeration on the ball after being thrown is
that due to gravity, which acts straight down.
Question 3, chap 4, sect 5.
part 1 of 4
10 points
A ball of mass 0
.
3 kg, initially at rest, is
kicked directly toward a fence from a point
20 m away, as shown below.
The velocity of the ball as it leaves the
kicker’s foot is 17 m
/
s at angle of 50
◦
above
the horizontal.
The top of the fence is 7 m
high. The kicker’s foot is in contact with the
ball for 0
.
03 s. The ball hits nothing while in
flight and air resistance is negligible.
The acceleration due to gravity is 9
.
8 m
/
s
2
.
20 m
7 m
17 m
/
s
50
◦
Determine the magnitude of the average
net force exerted on the ball during the kick.
Correct answer: 170 N (tolerance
±
1 %).
Explanation:
Let :
m
= 0
.
3 kg
,
θ
= 50
◦
,
v
0
= 17 m
/
s
,
and
Δ
t
= 0
.
03 s
.
From Newton’s second law,
F
avg
=
m a
avg
.
With
a
avg
=
Δ
v
Δ
t
,
F
avg
=
m a
avg
=
m
Δ
v
Δ
t
=
m
v
0
Δ
t
= (0
.
3 kg)
parenleftbigg
17 m
/
s
0
.
03 s
parenrightbigg
=
170 N
.
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 Spring '07
 KOPP
 Physics, Acceleration, Force, Friction, Gravity, Work, Correct Answer, fhand

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