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More Marilyn!

(January 19, 1998)
I know, I know. Once upon a time I accused Marilyn vos Savant, a syndicated columnist in the national magazine Parade, of being wrong, when it turns out I was wrong as well. But in the January 18, 1998 issue of Parade, she really is wrong, and also did not answer the question asked of her.

The question was: Wile E. Coyote is standing on a cliff which disintegrates under him. If he jumps off a big rock just before he hits the ground, he "stands a good chance of being only a couple of feet in the air at the time of impact [of the rock]". Will this help?

This is a variation on the classic elevator problem, which I have previously answered on my Mad Scientist page. The quick answer is: no. Just because you are not falling relative to the rock doesn't mean you aren't still falling relative to the ground! You might hit a teensy bit slower if you jump as hard as you can straight up, but the typical falling velocity of a person is about 200 kilometers per hour (about 120 miles per hour). You can't jump anywhere near that fast. If you're chasing a road runner, just be careful where you stand!

Marilyn's answer is that it won't work because you can't push off the rock. Her reasoning is that you are falling at the same velocity as the rock, and therefore "... will have no anchored floor to push against." This answer is incorrect.

The main reason she is wrong is because of Newton's Third Law: any reaction has an equal and opposite reaction. If Wile E. can get his feet on the rock (perhaps by grabbing it if it's close enough) and pushes, he will indeed move up relative to the rock, and the rock will move down. Another way to think of this is that he is making the rock move down a little faster, while making himself fall a little slower. As I said above, this still won't work, but not for the reasons Ms. vS gives. If she were correct, astronauts would not be able to push off the walls of the Space Shuttle! It's exactly the same problem; the Shuttle is in essence falling around the Earth at the same rate as the astronauts, which is why they feel like they are in freefall. But we know astronauts can jump off walls in the Shuttle; the problem is getting to the wall in the first place!

To be fair, the person asking the question asked if Wile E. could "jump up and down" on the rock, which is not possible. Once he jumped up, he would continue moving up (relative to the rock!), and would not fall back down on the rock. However, Ms. vS is still incorrect: she said "...Mr. Coyote will not be able to jump up at all." But he can, as I said above.

There is a website devoted to Ms. vos Savants errors, which may be of interest. There are also links there that deal with why people (hmmm, like a certain Bad Astronomer) sometimes enjoy it when she is wrong. Of course, I get email from people with a certain glee when I am wrong as well. What goes around... ;-)

©2008 Phil Plait. All Rights Reserved.

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