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(c) From
yg
t
=−
1
2
2
, we see that the ball has reached the height of
()
2
2
1
2

9.80 m/s
0.205 s

0.205 m
−=
at the moment the ball is halfway to the batter.
(d) The ball’s height when it reaches the batter is
2
2
1
2
9.80 m/s
0.409 s
0.820m
−
,
which, when subtracted from the previous result, implies it has fallen another 0.615 m.
Since the value of
y
is not simply proportional to
t
, we do not expect equal timeintervals
to correspond to equal heightchanges; in a physical sense, this is due to the fact that the
initial
y
velocity for the first half of the motion is not the same as the “initial”
y
velocity
for the second half of the motion.
40. We adopt the positive direction choices used in the textbook so that equations such as
Eq. 422 are directly applicable. The initial velocity is horizontal so that
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 Spring '08
 Any
 Physics

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