Physics 1A, Practice Problem 3
April 21, 2010
1 Free Kick (30pts)
You are charged with taking a free kick in the most important soccer game of the century. Your teammate
has been fouled a distance
D
g
= 30 m from the goal (see figure). In order to score a goal, you must clear a
wall of opposing player who are lined up a horizontal distance of
D
w
= 10 m from you. The height of the
“wall” is
h
= 1
.
8 m, and the height of the goal is
H
= 2
.
44 m.
h
= 1
.
8m
10m
H
= 2
.
44m
30m
θ
= 30
◦
(a)
If you usually like to kick the ball with an angle
θ
= 30
◦
with respect to the horizontal, with what initial
speed must you kick the ball to barely clear the wall of players
D
w
away?
Since the ball is in constant acceleration, we have
bracketleftbigg
x
(
t
)
y
(
t
)
bracketrightbigg
=
bracketleftbigg
(
v
0
cos
θ
)
t

1
2
gt
2
+ (
v
0
sin
θ
)
t
bracketrightbigg
the ball just clears the “wall” at some time
T
:
bracketleftbigg
D
w
h
bracketrightbigg
=
bracketleftbigg
x
(
T
)
y
(
T
)
bracketrightbigg
=
bracketleftbigg
(
v
0
cos
θ
)
T

1
2
gT
2
+ (
v
0
sin
θ
)
T
bracketrightbigg
Notice that we have two unknowns (
T
and
v
0
) and two equations. The rest of the problem is simply math:
no more physical information needs to be added. Even though this is a physics class (and not a math class),
I will still outline the mathematics to solve this problem.
Notice that
T
=
D
w
v
0
cos
θ
plugging into the second equation
h
, we get
h
=

1
2
g
D
2
w
v
2
0
cos
2
θ
+
D
w
tan
θ
so that
1
2
g
D
2
w
v
2
0
cos
2
θ
=
D
w
tan
θ

h
or
v
2
0
=
1
2 cos
2
θ
g
D
2
w
D
w
tan
θ

h
=
gD
w
2 cos
2
θ
1
tan
θ

h
D
w
or
v
0
=
radicalBigg
gD
w
2 cos
2
θ
1
tan
θ

h
D
w
= 12
.
8
m
s
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Physics 1A, Practice Problem 3
2
(b)
With what initial speed must the ball be kicked so that it not only clears the wall of players, but also
reaches
the goal at the minimum height of
h
⋆
= 2
.
1 m
,
just beyond the reach of the goalkeeper.
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 Summer '08
 Musumeci
 Charge, Acceleration, Friction, Velocity, Sin, Cos, Amin

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