53. We denote
h
as the height of a step and
w
as the width. To hit step
n
, the ball must fall
a distance
nh
and travel horizontally a distance between (
n
– 1)
w
and
nw
. We take the
origin of a coordinate system to be at the point where the ball leaves the top of the
stairway, and we choose the
y
axis to be positive in the upward direction. The coordinates
of the ball at time
t
are given by
x
=
v
0
x
t
and
yg
t
=−
1
2
2
(since
v
0
y
= 0). We equate
y
to
–
nh
and solve for the time to reach the level of step
n
:
t
nh
g
=
2
.
The
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 Spring '08
 Any
 Physics

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