So, I was reading about this guy Alexander Diem who set a skydiving speed record of 313mph. But nowhere did it tell me how long he spent in freefall. I calculated as follows.
313mph
*5280 = 1,652,640 feet per hour
/60, /60 = 459.0667 feet per second
So, I hear that falling bodies accelerate at 32fps/ps. I take this to mean that after 1 second in freefall you are travelling at 32 fps, after 2 seconds 64fps, after 3 seconds 96fps, etc etc. Which means all I have to do now is divide 459.0667 by 32 = 14.3458 seconds in freefall, assuming no wind resistance.
Am I correct? If so this would be the bare minimum amount of time, but wind resistance would have made it take a lot longer, yes? How do you work this out?
I also just realised I ignored the plane's initial speed as well. Ohhhhhh God.
There are formulas you can use, but they're the ideal ones, in that they ignore wind resistance. They are:
v = u + at
and
s = ut + 1/2at^2
Where
u = initial velocity in metres/second
v = final velocity in metres/second
a = acceleration in metres/second/second (9.8 metres/second/second when falling on Earth)
s = displacement (distance travelled) in metres, and
t = time in seconds.
313 mph = 140 metres/second (near enough)
So if wind resistance wasn't an issue, the time it would take to accelerate to 140 m/s would be:
140 = 0 + (9.8 x t), which is
140/9.8 = t, which is
t = 14.3 seconds (which I see agrees with your calculations)
Now, yes, this is a minimum time. Wind resistance would increase the time, though I don't know by how much, nor do I know how to work it out. It's affected both by altitude (which obviously changes as he falls) and his profile (spreadeagled people fall more slowly than people who form the shape of a vertical dart). What we do know is that eventually he'll reach terminal velocity - the speed at which air drag matches gravity - and he'll go no faster. In fact, as he falls, the atmosphere thickens, and his terminal velocity for his profile will actually decrease.
Also, because of the atmosphere, the higher the altitude he jumps from, the less drag the air will exert on him. However, using the second formula above, you can work out the minimum distance he must have travelled to reach his record speed. It's around 1000 metres. Obviously he would have needed plenty more distance beyond that to deploy his parachute and decelerate to a safe landing speed. But I'm pretty sure skydivers can jump from much higher than that sort of altitude.
The plane's initial speed is irrelevant, as it was flying horizontally, and the skydiver's speed is presumably his vertical velocity. The horizontal and the vertical are decoupled - your horizontal speed has no effect on how fast you fall (there's a simple experiment which demonstrates this: a device which simultaneously drops a marble while flinging another out horizontally - the two marbles hit the ground at the same time).
Incidentally, as for the record, I thought that was held by Joe Kittinger, who jumped from a helium balloon from an altitude of a few tens of kilometres, and broke the speed of sound while he was free-falling.
