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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 ofan oil tanker is to start with a large rectangular sheet ofsteel
that is
x
feet wide and
3x
feet long. Now cut a smaller square that is
t
feet on a side out ofeach corner of
the larger sheet and fold up and weld the sides ofthe 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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This note was uploaded on 03/02/2011 for the course ECON 101 taught by Professor Dannicatambay during the Spring '08 term at UPenn.
 Spring '08
 DANNICATAMBAY
 Microeconomics

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