A Matter of Utmost Gravity
Wile E. Coyote
Bleached Bones, AZ 59055
September 16, 1998
Math 236 Students
Norton, MA 02766
Dear Multivariable Calculus Students:
Oh, the pain and agony. Day after day. Week after week. Year after
year. I keep trying. But I just keep failing.
After much experimentation, I've decided to focus on one method
for gathering the main ingredient of my Aunt Edna's famous Roadrunner
Souffle: I'll use my handy catapult to
hurl an anvil and squash the little fowl as it comes around a blind curve.
When I went looking for help in my endeavors,
your enterprising and resourceful
professor naturally referred me to you.
One of the complicating factors in cartoon land that you may not be aware of
is that gravity not only has a vertical
component, but also has a horizontal component. I'm a pretty smart
carnivore, and I think could adapt my catapulting technique to this,
except that GRAVITY KEEPS CHANGING!
You know the way there are tide tables that tell you when high tide
and low tide are?
Well, here we have gravity tables that tell us what the horizontal and
vertical components of gravity will be.
There is some consistency in that gravity is always pulling
down and toward the west.
So, here's my plan:
I can set up the catapult near the blind curve
due west of the location in the road where the Roadrunner will be able
to see me for the first time.
Obviously, I'd like to squash the Roadrunner at that spot in the road,
and I'd like to be as far west as possible to increase
the element of surprise.
What I need to know is how far away I should set up the catapult,
the angle that I should launch the anvil, and
how long before the Roadrunner reaches the spot that I should shoot it.
Since I will launch it due east and gravity is pulling due west,
I really want to avoid the classic
scenario. I'd like to
know what angle I should ABSOLUTELY POSITIVELY avoid to escape this
As regular as clockwork, the Roadrunner zips down this road on
Saturday mornings at 11:00 am. I plan on launching my attack on
September 26 (at 11:00 am, of course) when gravity will be pulling down at
a rate of 9.8 m/s2 and to the west at a rate of 2.1 m/s2.
By the way, my trusty Acme catapult can
launch an average-sized anvil at 45 meters per second.
I've been down this road enough times before (pun intended) to realize
that everything may not go exactly as planned on the 26th. Since the
gravity is not always the same at 11:00 on Saturday mornings, I would
like formulas for each of my questions that only depend only the
horizontal and vertical components of gravity. That way, I'll still
be able to try my attack on another day.
In order to give me time to fine tune my instruments of destruction,
I will need your report by September 25. Please don't let me down.
Aunt Edna has been waiting a long time for this.
Hungry as ever,
Wile E. Coyote