rocketdodger said:
I say that discrete math could be used because that is what lazy people (and computer scientists like myself) use when we face a problem that elegant calculus might be able to solve. In this case, for example, we could break down the landing into, say, 100 discrete parts. Divide the 0.7 meters up into 100 0.07m parts, then assume the person will decelerate a certain amount over each part, up to the maximum force they can withstand. But I don't know what that force is, it was given to me, I don't remember it.
You need to use discrete math to solve this? And you were exposed to this in a mechanics class? I'm, um, appalled. At your instructor. There are a few simple equations that every high school physicist has to memorize.
ETA because something messed up with the browser.
delta v = acceleration * time.
Alternatively, the time of acceleration is the change in velocity divided by the acceleration. Princess Di died of a 70g deceleration, about 686 m/ss. To decelerate at half that rate, still definitely enough to shatter bones-- (35g, 343 m/ss), from 22.5 m/s would take about 0.0655 seconds.
The distance travelled by an object starting at rest with constant acceleration is 0.5 * a * t^2. This is also the distance travelled by an object in decelerating to a stop. An object decelerating at this rate would cover 0.74 meters, longer than the average leg is capable of bending to absorb the shock.
Our hypothetical jumper would be exposed to a minimum force of 35 gravities, furthermore, he would be exposed to it on the leg, which is much more fragile than other structures such as the rib cage. Not to put too fine a point on it, but there's no way that this person could escape without, at a minimum, a broken bone. More likely the person would be killed instantly.
Let's figure out what happens if this person misses his timing by so much as two hundredths of a second (so his effective deceleration time is 0.0455 instead of 0.0655 seconds). This, by the way, is superhuman precision -- human reaction time accuracy is usually measured in tenths of a second. In this case,
though, the person would be subject to more than 50 gravities of acceleration, enough to kill him instantly.