Ouch! They were SO close! They just needed to set those two equations equal to one another and solve for x. Since there is no energy lose due to friction of the ramp, and assuming a perfect spring, the potential of the raised block is equal to the potential imparted to the spring. The block momentarily stops at full spring compression and then is pushed by the spring and goes back to its initial 5 meter height. Conservation of energy at work.
We're just releasing CO2 into the atmo?!? These guys are the REAL cause of global warming! Couldn't we be capturing the CO2 for use? And stick a turbine on that tube to generate electricity.
Actually, that is perfectly safe from a physics standpoint. Any lateral motion to the left or right would be counter-balanced by the opposing cord. Also, we can see that the person is being "held" at a lower position to begin with. Since that is the maximum energy input in the down direction, they will never go lower than that. It's like the old demonstration of a hanging bowling ball. You take the bowling ball and walk with it to one side of the room and put it touching your nose and let go. The bowling ball will lose some energy to friction (air) and never be able to hit you.
Now, hold the bottle over the middle and let go. It will accelerate due to the gravitational field until relativity tells us that it becomes so massive that tidal forces tear everything apart.