Abbey Jump?!? Sorry, Mark, but you are already 50 feet or more down the cliff face… Perhaps you should have declared, “Abbey, we JUMPED!”
So much for suspense… we saw this coming days (weeks?) ago. Looks like the are sticking the landing, though, assuming that there is adequate depth of water to take the fall.
But let’s consider this answer from one who appears to have studied and paid attention in physics class… reminding us that water is hard, and it’s not the fall that will kill you, it’s the rapid deceleration upon impact… exerting multiple tons of pressure on the body…
Well, let’s look at the force of impact (granted it is in water, and calculating the true impact is quite complex)… nevertheless.
Let’s take the Golden gate bridge for instance:
67 meter fall/jump.
Weight of jumper: 70 kg
Let’s ignore air resistance:
We’re left with:
Acceleration = -9.8 m/s^2
Vf^2 = V0^2 + 2*a*h
= 0 + 2 * (-9.8) * 67
Vf = 36.24 m/s or 130.46 km/hr or 81 mph or 119.592 feet/s
F = ma = 686N
Since we’re jumping into water, let’s calculate the deceleration upon impact into water.
Impulse = -(70kg * 36.24m/s) = 2536.8 N . s
Ignoring terminal velocity and such (since it is 81 mph), so now it is just a matter of how you fall into the water to account for the amount of deceleration from the impact depth your body suffers.
We can assume that the density of a body is almost equal to water (considering we’re made up of roughly 3/4 of the stuff, and we float).
Impact depth = Length * (Density of body A / Density of the medium B)
So the impact depth is roughly the length of your body (plus a bit more).
For example: You were unlucky enough to fall perfectly horizontal.
This means the entire force of impact would cause your body to decelerate to half the velocity in about a foot of distance.
So at around 120 ft/sec, passing 1 foot of depth would take 1/120 = 0.008 seconds
Duration of impact would be 0.016 seconds:
Average Force = Impulse / dt = 2536.8/0.016 = 158550 N or 16 Tons.
Deceleration = Average Force / mass = 158550/70 = 2265 m/s^2 or 231 gs
Highly doubtful you’ll survive.
Now if you were lucky enough to fall feet first and perfectly vertical.
Impact depth = (let’s assume the person was 6 ft tall).
So 6/120 = 0.05 seconds
Duration of impact would be ~0.1 seconds:
Average Force = 25368 N or 2.6 Tons.
Deceleration = Average Force / mass = 25368/70 = 362.4 m/s^2 or 37 gs
If you did survive, the impact would be enough to shatter all your bones from your feet to your hips. There may be significant damage to your vital organs as well.
And for those of you still with me, a bonus. Here’s a great example of peer-pressure and dumb-assery… warning to the faint of heart, you may not want to click this link. Nothing malicious, it’s YouTube, but it’s pretty disturbing.