76
Part 1
Introduction
a.
How
does the value
of
t
at which the height
of
the ball is at a maximum depend on the
parameter
g1
b. Use your answer to part (a) to describe how maximum height changes as the parameter
g
changes.
c.
Use the envelope theorem to answer part (b) directly.
d.
On
the Earth
g
=
32,
but
this value varies somewhat around the globe. If two locations had
gravitational constants that differed by 0.1, what would be the difference in the maximum
height
of
a ball tossed in the two
places1
2.6
A simple way to model the construction
of
an oil tanker is to start with a large rectangular sheet
of
steel
that is
x
feet wide and
3x
feet long.
Now
cut a smaller square that is
t
feet on a side
out
of
each corner
of
the larger sheet and fold up and weld the sides
of
the steel sheet to make a traylike structure with no top.
a. Show
that
the volume
of
oil that can be held by this tray is given by
V
=
t(x

2t)(3x

2t)
=
3tx
2

8t
2
X
+
4t
3
.
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 Spring '08
 DANNICATAMBAY
 Microeconomics, Optimization, oil tanker, maximum height changes

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