PHYS 2210
UNIVERSITY OF COLORADO AT BOULDER
CLASSICAL MECHANICS AND MATH METHODS, SPRING, 2011
Homework 2
(Due Date: Start of class on Thurs. Jan 20 )
NOTE:
Be sure to show your work and explain what you are doing. (Correct answers, for which we cannot
follow the work, are worth no credit).
1.
(4 pts) A particle is projected with velocity
v
0
straight up a slope which makes an angle
α
with the horizontal.
Find the time required to return to the starting point. (assume frictionless motion) Explicitly check the units
of your final formula, and discuss the special cases
α
→
0 and
α
→
90
◦
.
2.
A soccer player kicks the ball with a velocity
v
0
at an angle 45
◦
(to reach maximum range). She want to
kick it in such a way that it barely passes on top of two opposite team players of height
h
(12 pts: 4+4+4).
(a) Show that if the separation between the two opponents is
d
≤
v
0
g
v
2
0
−
?
gh
, the soccer player succeeds.
(What is the numerical value of the ? in this formula?)
(b) Use Mathematica to plot
d
as a function of
v
0
, setting
h
= 2
m
.
Hint: If you want to plot a function
f
[
x
]
vs
x
with
x
0
< x < x
1
with Mathematica you can use the instruction
Plot[
f
[
x
]
,
{
x, x
0
, x
1
}
]
. Sqrt[] is the
syntax for square roots. Note that Mathematica can’t plot a function with symbolic coe
ﬃ
cients (so you
have to plug in the values for both
g
and
h
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 Spring '11
 STEVEPOLLOCK
 mechanics, Work, Coordinate system, Spherical coordinate system, Polar coordinate system, unit vectors

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