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I have heard that a man can fall faster than the speed of sound, and survive, by jumping from 36,000 meters; a free fall that, it seems, lasts ten minutes after the jump. Is it true?

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If you mean "and survive" we'll find out this week: space.com/17927-record-supersonic-skydive-attempt-delay.html – Larry OBrien Oct 6 '12 at 18:43
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We'll find out on Tuesday, when Felix Baumgartner will attempt the jump‌​. – Yannis Oct 6 '12 at 18:43
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@LarryOBrien - The "and survive" part is open to a lot of interpenetration though, are we talking just breaking the sound barrier and surviving or are we also including a successful landing? – Rob Z Oct 6 '12 at 19:12
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Do you have some reason to believe that the folks who have--presumably--done some calculations on this are wrong? I really object to "I don't know anything about <subject>, but it doesn't seem right to me" posts. I mean, so what? Argument from ignorance is boring and deeply unconvincing. – dmckee Oct 6 '12 at 21:42
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@dmckee there's also the possibility that the organizers may be over-hyping the event. It'd be nice to see confirmation of the claim by relatively impartial individuals. – Andrew Grimm Oct 7 '12 at 7:00
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up vote 27 down vote accepted

Can a man fall faster than the speed of sound?

Update (15 Oct 2012): Definitely, yes - 372.8 m/s, or Mach 1.24,

Yes, almost certainly, though none have yet (7 Oct 2012) in any well-published verified account.

on Aug. 16, 1960, Capt. Kittinger jumped from a height of 102,800 feet, almost 20 miles above the earth. With only the small stabilizing chute deployed, Capt. Kittinger fell for 4 minutes, 36 seconds. He experienced temperatures as low as minus 94 degrees Fahrenheit (-70 degrees Celsius) and a maximum speed of 614 miles per hour. … The 28-foot main parachute did not open until Capt. Kittinger reached the much thicker atmosphere at 17,500 feet.

From http://www.nationalmuseum.af.mil/factsheets/factsheet.asp?id=562

That is 274 m/s at some point during a descent from 31333 m to 5333 m altitude.

Speed of sound graph

From http://en.wikipedia.org/wiki/Speed_of_sound

From this graph we can see that if you start at 36000 metres, when you have fallen 16000 metres to 20000 metres height, the speed of sound is 295 m/s. Kittinger's maximum speed was 274 m/s at unstated altitude. It seems plausible that someone might be able to travel 7.6% faster oriented head down with no stabilising chute.

There are reports that say Kittinger in 1960 reached supersonic speeds - e.g. Airforce Magazine - but in a BBC video (at 02:10) Kittinger says he was "very nearly supersonic").

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Fixed units - please use metric units in the future. Most users of this site are not familiar with uncommon units of measure such as imperial. – Sklivvz♦ Oct 7 '12 at 12:46
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@Skliwz, I changed to SI units (the universal language of science) except where needed to preserve the integrity of quotations. The units are not important to my answer, it is the smallness of the required percentage improvement I am trying to show. – RedGrittyBrick Oct 7 '12 at 13:41
We already have a faq-level policy (meta.skeptics.stackexchange.com/q/1001) on meta. You may want to move your "note on units" over there :-) – Sklivvz♦ Oct 7 '12 at 14:26
@Skliwz: Thanks, done. – RedGrittyBrick Oct 7 '12 at 14:39
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Yes!

BBC News reports:

Austrian Felix Baumgartner has become the first skydiver to go faster than the speed of sound, reaching a maximum velocity of 833.9mph (1,342km/h).

In jumping out of a balloon 128,100ft (24 miles; 39km) above New Mexico, the 43-year-old also smashed the record for the highest ever freefall.

The whole thing is part of Red Bull Stratos project. Highlights video is available on YouTube, there will be the National Geographic documentary "Space Dive" released later on.

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Unfortunately weather didn't permit the launch, although right now the conditions are reported as improved. Check here for live(ish) status updates: redbullstratos.com/the-mission/launch-progress – Yannis Oct 10 '12 at 3:27
I think this answer should now start "Yes". – Jamiec♦ Oct 15 '12 at 7:39

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