Douglass Houghton Workshop, Section 1, Wed 10/19/10
Worksheet Indefatigable
1. Suppose you are asked to design the first ascent and drop for a new roller coaster at
Cedar Point.
(You get to name it, too!)
By studying photographs of your favorite
coasters, you decide to make the slope of the ascent 0
.
8 and the slope of the drop

1
.
6.
You decide to connect these two straight inclines
y
=
L
1
(
x
) and
y
=
L
2
(
x
) with part
of a parabola
y
=
f
(
x
) =
ax
2
+
bx
+
c
, where
x
and
f
(
x
) are measured in feet. For the
track to be smooth there can’t be abrupt changes in direction, so you want the linear
segments
L
1
and
L
2
to be tangent to the parabola at the transition points
P
and
Q
.
To simplify the equations, you decide to put the origin at
P
.
(a) Name your coaster.
(b) Suppose the horizontal distance between
P
and
Q
is 100 feet. Write equations in
a
,
b
, and
c
that will ensure that the track is smooth at
the transition points.
(c) Solve the equations in (1b) for
a
,
b
, and
c
to
find a formula for
f
(
x
).
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 Winter '08
 Conger
 Graph Theory, Derivative, dead zombies

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