Basic Understanding
Do you know why when you fall down from a tree horizontally it hurts, but not so much when you fall down vertically, meaning you stand on your legs?
Well... according to Newton's law of gravitation, he said force is a mass time acceleration (F = MA).
Let's think of it this way: when you (for some reason) are on top of a tree, do you feel like you are getting pulled down by an invisible force? That force in the physics world is known as gravitation, which many of us call weight. The force of gravitation can be calculated by:
g x M where g is a constant of gravity (9.81 m/sec^2)
and M is a mass of your whole body (including your clothes, shoes and whatever you have on).
Note: Weight (in Newton's) is mass x acceleration. Mass is not weight!
Now, (g x M ) is a force, therefore F = (g x M). Put this back into Newton's Law we get
F = MA >>> (g x M) = MA
Now, let us think, when you sit down on a chair, where would your center of the mass be?
Your center of the mass will be on your butt where it is on top of the chair, right?
Because the gravity is pulling all of your weight down, but the chair is preventing you from falling to the ground, all your weight will be stuck at your butt.
When you are falling down, while you are in the air, there is no chair to block you from falling down. Therefore, you get pulled all the way to the ground...
Think of the ground as a chair that is blocking you from getting pulled all the way toward the center of the Earth.
Look at the figure above, where Homer appears more unhappy in figure (A) than in figure (B).
That is because he knows that if he landed in horizontal position, as show in (A), he would hurt himself a lot more than in (B) position.
Think of each arrows as gravity forces that are pulling Homer down. If he landed as (A) position, his whole body would suffer the highest impact because his center of the mass will be hitting the ground.
While in vertical (B) where his center of the mass is somewhere around his belly, not his butt... When he landed, his belly (center of the mass ) did not touch the ground, only his feet touched the ground. Therefore, his feet will be the only area that suffered the most impact from falling, while his center of the mass will feel a little bit of impact. That is why we don't suffer much from falling down the tree if we land on our feet.
And of course, we may not survive at all if the tree was, say, over 30 feet tall... but that would be a different story.
While you were falling, the potential energy of your whole body due to the height of gravitational force is converted into kinetic energy (energy of motion). It's an interesting process to watch. We can also calculate the speed of our falling body before we hit the ground, which is really simple.
since F = MA, and F is your mass time constant of gravitational, which is 9.81 m/sec^2
so, F = MA --> A = F/M ---> A = (Mg)/M = g ----> A = g = 9.81 m/sec^2
Which explains why a big rock and a small rock fall to the ground at the same speed, which is 9.81 m/sec^2
