This is clearly a bungee-jump question, as in bungee-jumping there are five states:
1) Preparation, where you are stationary on the base surface, but getting ready to jump,
2) Jumping, where you are free-falling to approach terminal velocity,
3) Oscillating, where you are bouncing like a puppet on the end of the bungee,
4) Suspended, where you have come to rest at the end of the bungee, and
5) Retrieval, where you get back to the base surface.
To determine the longest time to suspended, you have to determine the longest bungee jump from a stationary base (as jumps from a moving base like a helicopter never fully come to the suspended state). This is the Royal Gorge Bridge in Colorado, which is about 100 meters taller than the next tallest stationary base bungee jump, meaning that the length of the bungee at full extension is probably 900 feet. Sadly, there's little recorded data of the length of oscillation - most video online, such as
link, focus pretty much entirely on the duration of the jump and not the oscillation, so we can only calculate an approximate answer of three minutes, 13 seconds. It might actually take longer or shorter with different types of bungees, as well as other variables such as how much the jumper is moving, how much wind there is, even the elevation above sea level. But note that most bungee jump companies will not let their jumpers oscillate for that long; after the first few bounces, they will typically begin retrieval, letting the jumper down the rest of the way to the ground or hauling him back up to the base. In those circumstances, the jumper can not be said to have actually achieved the suspended state.
Thanks! That was a very interesting question!
