134. Suppose that you fall out of a plane about 30 seconds after your parachute pack fell out. Is it really possible to catch up to your parachute pack and save yourself?
The answer depends on how high the plane was flying and just how much air resistance the pack experiences as it falls. After a few seconds of falling, an object reaches a terminal velocity—it stops accelerating downward. That's because the upward force that air resistance exerts on it grows stronger as its downward velocity increases. Eventually, the upward force it experiences exactly balances its downward weight and it has no net force on it—it doesn't accelerate. For a person, this terminal velocity ranges from about 100 mph to 200 mph, depending on the person's shape. Curling into a compact ball should allow you to reach a relatively high terminal velocity of 200 mph. Since the parachute pack is relatively light but has substantial surface area for the wind to push against, it probably has a lower terminal velocity of say, 100 mph. This arrangement would allow you to approach the pack at a relative velocity of 100 mph. In order to actually overtake the pack, you'll still need some time, so the higher the plane was when you started, the better your chances are. Since the pack has a 30 second head start and descends at 100 mph, it will be about 0.83 miles below you when you leave the plane. You'll catch up to it 30 seconds later, during which time you will have dropped a total of 1.67 miles. Thus in principle, you could catch the pack so long as the plane's altitude was more than about 1.67 miles. To allow time to put the pack on, for the parachute to open, and for your terminal velocity to then become low enough to avoid injury, you'd better have the plane at more than about 2.5 miles. Still, this doesn't sound like a fun experiment.