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assuming that a person lies flat on top of a table and uses it to jump from a building of height 20-30 meters, will the legs of the table absorb the forces of the fall and leave the person uninjured, since the person didn't suffer any direct hits to the ground and got protected by the head of the table?

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  • $\begingroup$ In a desperate condition I would try using a spring mattress $\endgroup$ – anna v Mar 8 '20 at 6:42
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The body itself does not need to directly hit the ground. Its the impact force transmitted to the body that counts.

The table legs would have to absorb enough of the impact energy so that the impact force transmitted to the body does not result in a fatal injury. This is the reason that automobiles are designed with crumple zones to absorb energy in a crash and lengthen the stopping distance of the vehicle, both of which reduce the impact forces transmitted to the body. The underlying principle is the work-energy theorem.

Suffice it to say that table legs are not designed to absorb energy in a crash.

Hope this helps.

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I don't know the stress a bone is able to withstand before fracture. However, a simple approximation yields that it is possible to survive this fall:

Let's assume that we are falling $h_1=29m$ and that we deaccelerate constantly during the last $h_2=1m$. In this scenario we obtain the energy $E = m g h_1$ during the free fall and experience the deacceleration $$ a = F / m = E/(m h_2) = {h_1 g}/{h_2} = 29 g $$ during the last $1m$. This deacceleration last for $t = \sqrt{2 h_2/a}\approx 84ms$. Taking wikipedia as reference this is tolerable by humans.

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  • $\begingroup$ It's not the deceleration that is the concern. It is the impact force on the body when the table impacts the ground. $\endgroup$ – Bob D Mar 7 '20 at 17:30

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