WELCOME
TO GUIDO'S HOT AIR BALLOON RIDE SERVICE! GUIDO AND HIS FRIENDS HAVE
A PROBLEM THAT THEY ARE HOPING YOU CAN SOLVE USING YOUR KNOWLEDGE OF THE
PYTHAGOREAN THEOREM.
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The
problem: Guido and two of his friends (creatively
known as buddy "A" and buddy "B") are flying in their individual hot air
balloons 2,000 feet above some huge, scenic South American lava pits, with
the buddies' two balloons flying at right angles to Guido's balloon.
Recognizing the geography and topography of the area, Guido knows
that his balloon is approximately 100 yards from buddy A's balloon.
Guido, having learned of a super excellent helium sale, has just screamed
out in glee. Buddy A heard the euphoric excerpt after a ONE second
delay, while buddy B heard the scream after a THREE second delay.
Unfortunately, just as Guido turns back to go pick up a client, buddy
A realizes he (buddy A) is low on fuel and must simply remain in place
(moving uses a great deal more fuel than remaining stationary, and so is
not a feasible option) while Buddy B can hopefully move over to pick him
up before his balloon sinks into the suddenly not-so-appealing lava
pits below. Buddy B is also low on fuel, but has enough to travel
about 325 yards before heading for safety. Should buddy B try to
rescue buddy A, or must he abandon him in order to save himself???
Diagram
1 below represents an overhead view of the three hot air balloons and some
of the information given in the problem. Use the diagram, the given
information, and the Pythagorean theorem to determine if buddy A is toast.
Diagram 1
What do
you think? Can buddy A be saved? After attempting a solution,
click on the appropriate link below: