This is of course being a little silly, but it does get the physics wrong. Your energy is proportional to the square of your speed, so you have 25x more energy to dissipate at 120 mph, not 5x. Even if your five point landing was perfect, each of the five 'hits' is the equivalent of a landing at just under 60 mph, not 24.
In the case of you landing, I don't think energy balance is the way to look at it; each of the collisions that slows you down will transfer some energy to the ground. In terms of force, the force is dependent only on the acceleration, so it comes down to how long each impact lasts. If each "bounce" or "thud" lasts the same amount of time (I don't know if this is realistic) then each one will transfer 1/5th of the force, as the article says.
Potential energy is linear with height. AKA it takes the same energy to climb from floor 1 to 2 as 2 to 3.
Gravity is 32 feet per second per second aka you gain speed over time. In a vacuum 0 to 32 feet per second takes 1 second, 32 to 64 feet per second takes 1 seconds, 64 to 96 takes 1 second etc.
However, in the first second you fall 16 feet. in the next second you fall 38 feet because you where falling at the start of that second. Thus, it takes more energy to increase your speed.
PS: What's confusing about rockets, is your fuel has momentum. So, when use it your consuming the energy it took to get that fuel up to speed with you. Further, at low speed most of the energy goes into the exhaust not the rocket.
Doesn't make sense. Care to explain? Are you saying it takes less energy to take an object from 0 to 10m/s than it requires to take it from 10m/s to 20m/s?
E = 1/2 m*v^2
dE = E1 - E0 = 1/2(10^2) - 1/2(0^2) = 50J
dE = E2 - E1 = 1/2(20^2) - 1/2(10^2) = 200 - 50 = 150J
v = sqrt(2*E) = sqrt(200) = 14.1m/s
You can find plenty of examples but that's about it. Ex: You hold a gun in your hand and shoot it, the gun kicks back because momentum is concerved. But, the bullet is a lot more dangerous than the gun because while it has the same momentum it's got a lot more energy. Now, it hits a bullet proof vest. The vest still hits the person wearing the vest but because it obsorbed the energy it feels like a strong punch instead of making a hole in them.
A second gust at 10 m/s is NOT enough to further accelerate the balloon to 20 m/s. Because the wind and the balloon are now travelling at the same speed. It follows intuitively that the second gust should contain more kinetic energy than the first gust.
Say m=2 so we're just left looking at the v^2 terms:
120^2 - 96^2 >? 24^2 - 0^2
5184 >? 576
So yes, the KE difference between 120 and 96 is greater than the difference between 24 and 0.
*KE == kinetic energy
kinetic energy: "energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes."
in normal person terms: the energy of moving, or ~exercise, in a parallel world :)