But, you ask, is 1.845 seconds enough time to see my life flash before my eyes? In other words, the last question,
Will it make you die?
Probably yes. Try riding your bicycle into a wall at 30 mph (make sure you’re not clipped in). While someone might know a little more about this than me, we can pretty much only guess how quickly you’ll be stopping. This, and your mass, determines the amount of force you’ll receive from the wall when you die.
The impulse (change in momentum) for a 150-lb person going from 42.43 ft/s to 0 ft/s is (42.43 * 150 ) 6360 ft-lb/s. This should actually be in ft-slug/s, to get 200 lbf-s. I’m switching to SI anyway.
Using the heavier 70-kg SI human, the impulse is 900 N-s. Your velocity on impact is 12.93 m/s . Somewhere around a 12 kN force is what I’ve heard will kill you. To get average force, we need an estimate of time.
If you go splat like Wile E. Coyote (i.e. the wall stops you completely), I’d guess your body would stop in something like 10 mS. The force of this is 90 kN, easily enough to kill you and make a not-so-pretty cliff ornament.
More likely than not, though, you’ll bounce. If you bounce, the impulse is actually larger but the amount of time will certainly be longer. So if you bounced back high enough to swing 1 m up, the impulse is now 1200 N-s. But maybe you took more than twice as long, say 25 ms. This gives a force of about 50 kN. Still enough to kill you, but it’s a bit more pleasant to look at for the rest of us.
[diversion on climbing ropes : static vs. dynamic]
Now for something else : Suppose you just fell of the east side of the canyon, not the west side. In other words, straight down. Do you still die? Of course, it just happens sooner. Your rope is inelastic, so you get the same impulse in about the same amount of time.
Let’s say your rope is slightly elastic; it only stretches 0.5%. That’s 2 in. on 30 ft. You go from full speed to stop in this distance, and the average force is 130 kN. Your organs are mush.
If, however, you were using a normal rock-climbing rope (a dynamic rope), you might expect it to stretch about 7% (manufacturers will specify). This is 25 in. on 30 ft. You take about 100 ms to stop, and experience a force of only 9.8 kN. This is serious, but probably not deadly. At any rate, you’ll actually be bouncing on this rope, so the force will be a lot less.
The point of this is, don’t go climbing on cheap ropes. And if you’re on a static rope, make sure you’re not going to fall.
[/diversion on ropes]