PHY131 MidtermI Exam
February 26, 2003
Solutions
1) (20 points) A soccer player kicks the ball at an angle
θ
of
40
ο
with respect to the
level playing field. The ball travels a horizontal distance of 45 m before hitting the
ground. (Hint: the trigonometric identity
)
2
sin(
sin
cos
2
θ
θ
θ
=
might be very useful
here!)
a)
Determine the initial speed of the ball at t = 0.
v
0
θ
x
y
0
d
s
m
gd
v
g
v
g
v
t
v
t
x
d
g
v
g
v
t
gt
t
v
t
y
t
v
t
v
t
x
d
d
y
d
y
x
2
.
21
)
2
sin(
)
2
sin(
)
sin(
)
cos(
2
)
cos(
)
(
)
sin(
2
2
0
2
1
)
(
)
cos(
)
(
0
2
0
2
0
0
0
0
2
0
0
0
=
=
⇒
=
=
=
=
⇒
=
=
⇒
=
−
=
=
=
θ
θ
θ
θ
θ
θ
θ
b) When does the ball hit the ground?
s
g
v
t
d
78
.
2
)
sin(
2
0
=
=
θ
c)
What is the ball’s velocity vector at maximum height?
s
m
v
v
v
s
m
v
x
x
y
2
.
16
)
cos(
0
0
0
=
=
=
=
θ
d)
What is the acceleration vector at t = 0, at maximum height, and when the ball
hits the ground?
cases
three
all
for
0
2
g
a
s
m
a
y
x
−
=
=
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2) (20 points) During last week’s snowstorm, you were worried about parking your car
in your driveway, which has an incline of 12
o
. Your neighbor John’s driveway has an
incline of 9.0
o
, and Jill’s driveway across the street has an incline of 6.0
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 Spring '03
 Rijssenbeek
 Physics, Acceleration, Mass, Velocity, Jill

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