A Matter of Utmost Gravity

Wile E. Coyote
Bleached Bones, AZ 59055
September 16, 1998

Math 236 Students
Wheaton College
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 anvil-goes-up-in-the-air-and-lands-on-poor-Wile-turning-him-into-an-accordion scenario. I'd like to know what angle I should ABSOLUTELY POSITIVELY avoid to escape this fate.

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