Jonathan C. answered • 10/16/19
Experienced Tutor and TA, Bachelor's in Physics
So there's a lot to this question and it's actually pretty fun and interesting. When a skydiver jumps off a plane, they're experiencing two main forces: gravity and air resistance. The motion of the skydiver is going to depend on how these two forces balance each other out.
The moment the skydiver, let's call them Alex, jumps off a plane, they're experiencing a gravitational acceleration of around 9.8 m/s^2, and not much friction since they're falling pretty slowly at that very instant. As you can imagine with such a high acceleration, though, they start falling very fast very quickly. The negative acceleration (or deceleration) that comes from air resistance is proportional to the velocity when the object is moving slowly, but proportional to the velocity squared as it moves more quickly. What this means is that as Alex gets faster and faster because of gravity pulling down on them, the force of air resistance pushing up on them gets bigger and bigger.
Eventually, the force of air resistance will get so large that it'll perfectly balance the force of gravity, and when this happens, the acceleration on Alex will be 0. This is not to say that their speed will be 0, but rather that the change in their speed will be 0, so their speed will stay the same (or constant). This maximum speed is known as "Terminal Velocity", and it depends on a bunch of factors, it's the reason why parachutes work and why cats can survive being dropped off tall buildings (but not the second floor). It depends on a bunch of factors. For example, if Alex is spread out, front facing down and arms and legs open, then they'll likely have a terminal velocity of around 120 mph. If they decide to dive down head first, then the terminal velocity can go up to 150 to 180 mph.
Now how about what happens when all the skydivers reach that speed and are hanging around doing tricks in free fall, then decide to hook together. This then becomes a conversation about relativity, but the simpler kind, not the Einstein kind. If they're all traveling at the same speed (or close enough), we can say that they're falling speed relative to each other is basically zero, and if they're not moving horizontally, that they're all just still in that reference frame. Let's say, then, that someone decides to lean in to move closer to someone else. To the other person, the person leaning is just slowly moving closer to them. Even though everyone's falling at 120+ mph, to each other, they're not actually moving that fast relative to each other, so when they get closer to each other and link together, the forces they're applying on each other aren't strong enough that they'd get hurt.
Finally, someone, let's say Alex, decides they've had enough and they pull they're cord, opening the parachute, and woosh! Up they go, flying! Except what really happens is actually a bit different. When Alex deploys the parachute, it opens up, and what happens is that the force of air resistance on Alex becomes enormous compared to what it was before. Since air resistance depends on the surface area of the thing falling, and a parachute has way more area than the average body of a person, it makes sense that opening a parachute will drastically increase their air resistance. For this moment, very quickly, gravity and air resistance will no longer balance each other out as before. Instead, the stronger air resistance means that the terminal velocity will be much lower than it was, but since Alex is already traveling much faster than it, the air resistance will quickly overpower gravity so that they will slow down to the new terminal velocity, and balance each other again. To everyone else, it looks like Alex has shot up into the air, but in reality, they just slowed down to a new terminal velocity; at no point did Alex really move up.
I hope this helps clear things up, and if you have any other questions, let me know!
-Jonathan
