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34. The distance the marble travels is determined by its initial speed (and the methods of
Chapter 4), and the initial speed is determined (using energy conservation) by the original
compression of the spring. We denote
h
as the height of the table, and
x
as the horizontal
distance to the point where the marble lands. Then
x = v
0
t
and
hg
t
=
1
2
2
(since the
vertical component of the marble's “launch velocity” is zero). From these we find
xv
h
g
=
0
2
. We note from this that the distance to the landing point is directly
proportional to the initial speed. We denote
v
0 1
be the initial speed of the first shot and
D
1
= (2.20 – 0.27) m = 1.93 m be the horizontal distance to its landing point; similarly,
v
02
is
the initial speed of the second shot and
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Energy

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