Why does it hurt more to fall from 10 stories, than 1? F = m a. Falling from any distance, mass stays the same, and acceleration due to gravity stays the same. So, why does it hurt more, the longer you fall?

Question

Why does it hurt more to fall from 10 stories, than 1?  F  =  m  a. Falling from any distance, mass stays the same, and acceleration due to gravity stays the same. So, why does it hurt more, the longer you fall?

apopihvj · Accepted Answer

Yes,   F  =  m  a, but also   v  =  a  t. That means that, as you fall for a longer time, your speed will increase.After 1 second, you are going at   9.8  m      /    s or   35  k  m      /    h, about the speed of Usain Bolt. After 10 seconds you would reach   98  m      /    s  e  c or   350  k  m      /    h. For a free-falling human, the air resistance actually limits you to about   200  k  m      /    hWhen you hit the ground, the deceleration is always going to be a lot more than   1  g, as the ground tends not to give way. From small heights, your muscles can take the strain; for higher speeds your bones will snap, and at very high speeds, you will not only break lots of bones, but your brain will decelerate so fast that it will stop functioning. That will kill you instantly.From 10 floors up (say   30  m) you will hit the ground after   1.7  s, at a speed of   9.8  ∗  1.7  =  17  m      /    s or   60  k  m      /    h. Try driving into a wall at that speed. In a modern car you may survive it but, without the seatbelt, airbags and lots of steel around you, you are almost certainly dead.To recapitulate, it&#039;s the deceleration that hurts you, and that becomes larger as your speeds gets higher and the ground does not start to give until you reach speeds much higher than what will kill you.

Clara Dennis · Accepted Answer

Let me summarize the discussion in the comment section. First of all you can safely use Newtons equation of motion  F  =  m  gwith a constant gravitational acceleration   g. This is simply because the height of a 10 stories building, lets say   30  m, is still very very small compared to the radius of the earth which is about   6000  k  mTherefore, as you correctly say, the acceleration during the fall is constant and as a consequence the speed   v increases linearly with the duration   t of your fall  v  =  g     tIf you are familiar with the concept of energy: the potential energy of your initial position is converted to kinetic energy during your fall and when you want to stop again you have to get rid of this energy.When you hit the ground there are different possibilities for the kinetic energy to go away. For example the deformation of the ground you are landing on (it surely makes a difference if you land on concrete or on a trampoline), but also deformation of you (that&#039;s what hurts).If you now fall from a greater height you will have more kinetic energy at the moment of your impact and you and the ground will deform more. Unfortunately, the ground will usually deform much less then you do and it will hurt you more.

Why does it hurt more to fall from 10 stories, than 1? F=ma. Falling from any distance, mass stays the same, and acceleration due to gravity stays the same. So, why does it hurt more, the longer you fall?

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