There are countless videos showing BMX/freeride/downhill etc. riders jumping and dropping from heights. For the unprofessional spectator, they seem impossible to survive. From the physical point of view, the bike reaches the ground with a given kinetic energy which is dependent on the height of the drop and on the combined mass of the rider and the bike. Where is all this energy dissipated? I assume that most of this energy is absorbed in the bike, and some by the rider. How is this energy distributed in various components of the bike?
When you combine all of these elements in harmony you've got a really substantial amount of movement, and although it only takes a fraction of a second to land a big jump, it's enough time to slow down a rider's mass and keep them from becoming a grease spot at the bottom of The Tooney Drop.
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You mentioned KINETIC ENERGY, which obviously have to go somewhere. Sometimes you have reception, and the bike comes at speed, but sometimes, like in bike trial, the bike lands "flat" on plain concrete. Sometimes, too, freeriders land on flat concrete at speed, and at least the vertical component of the drop's kinetic energy disappears.
I would say there are only three places where this energy can go:
It is important to mention that rigid elements of bike (frame, wheels) don't take up the kinetic energy, only transmit forces to somewhere else. Also, just to add to what @jm2 said, the joints only transmit the forces and (fortunately) don't take up any significant amount of energy: the landing kinetic energy is couteracted by muscle contraction acting through the joint.
As already stated by jm2...there are many reasons riders can take bigger drops. However as your question was how is it distributed...
Look at the swing arm for an example...vertical impact of the bike causes the rear lower stay to move upwards from the pivot point at the crank. That movement (force) is redirected to the upper rear stay and transferred to the shock that absorbs the majority of the force before finally transferring the last amount to the seat tube at a perpendicular angle to the rider not up through the rider.
That's why the full force isn't placed directly on the riders legs.
The geometry is what's splitting the lion's share out to 10 inch shocks which allow the rider to drop 20 feet without destroying the bike first and then being left with a much smaller amount of energy to suck up in his/her legs and arms.