Computer Algebra Recipes

4.3. VARIATIONAL CALCULUS MODELS 195
4.3.3 The Human Fly Plans His Escape Route
A product of the untalented, sold by the unprincipled
to the utterly bewildered.
Al Capp, American cartoonist, comment on abstract art (1907{1979)
Mr. X, whom the popular press have dubbed the \human °y," plans to scale the
outside vertical wall of one of Metropolis's tallest skyscrapers, the Metropolis
Stock Exchange, using a combination of his rock-climbing skills and suction
cups. Knowing that once the climb has begun, the police will quickly learn of
his exploit and try to capture him, Mr. X plans to execute a daring escape.
He intends to evade the law enforcement o±cers by sliding down a thin, but
strong, wire to a yet-undetermined window at a lower elevation in the slanted
roof of the Museum of Modern Art directly across the street (see Figure 4.16).
The window will be left open so that Mr. X can zoom through to the room in-
y
Figure 4.16: Mr. X sliding down wire with a police helicopter hovering nearby.
side, brake rapidly, and make a (hopefully) relatively soft landing on the °oor.
Catching the police by surprise and taking advantage of the museum's many
exits, Mr. X hopes once again to avoid capture and expand his ever-growing
legend. However, being somewhat cautious, despite an otherwise harebrained
scheme, Mr. X decides to check the details of the escape route by conferring
with his mathematician friend Mike.
\Mike, the roof of the stock exchange is slightly over 200 meters above
street level and the police will surely be waiting for me on the rooftop and in
the street below. They will probably even have a police helicopter hovering
nearby. If I were to connect a wire to the stock exchange outer wall at the 200
meter point, what shape should the wire have, and what point on the slanting
x