Jumping To Prevent Crashing

Why Jumping Is A Useless Thing To Do When Your Cliff Or Elevator Crashes

by Joseph Francus Nebus (nebusj@axiom.math.rpi.edu)
written 28 Nov 1994

This article is classified "Real"


Suppose you are somewhere in the desert -- Arizona, say, or possibly
New Mexico -- and are chasing, say, a roadrunner as you are simply
famished.  You plan to catch the roadrunner by throwing a large boulder
onto its head from a cliff, but, as you are pushing the boulder over the
edge (using a lever, naturally), the cliff breaks off.  You finally push
the boulder off to notice that the ledge you were on is falling down the
*very* deep ravine.

Question: Is it to your advantage to jump off the bit of ledge remaining
right before it his the ground, so that you can cancel the speed of your
fall and keep from being squashed flat?

Answer: Not unless you can jump hard enough.  Let's assume, for the sake
of simplicity, that the falling ledge with you on it reaches a terminal
velocity (that is, the acceleration of gravity is exactly cancelled by
the wind resistance, so it does not fall any faster) of about 50 meters
per second.  That means that you, too, are falling about 50 meters per
second.  To avoid getting smashed when you hit the ground you need to be
going down at about 0 meters per second.  So you need to jump up with a
speed of about 50 meters per second.

So, unless you are able to jump hard enough to cover 50 meters -- half
the length of a football field -- in one second; or, to put it another way,
to (from rest) jump up 125 meters -- more than the length of a football
field -- then you are going down too quickly to cancel out your velocity
and save yourself.

Besides, even if you did, the boulder you pushed off would then smack you
on the head, and it would be going about 50 meters per second, even if you
held up a little umbrella to protect yourself.

See also:
  • Jumping Off Cliffs And Other High Places

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