Can you skydive at 40000 feet?

Answer 1

No, since the air is too thin - there is not enough oxygen to breathe.

It can be done, but you have to wear an oxygen mask. The military does HALO (high altitude, low opening) jumps from 35,000+.

Answer 2

Yes you can. In the military they have Airborne soldier with the certificate call HALO (High Altitude Low Opening). Troops are typically dispatched from altitudes between 15,000 feet (4,600 m) and 35,000 feet (11,000 m) The United States Parachute Association (USPA) indicates that a partial pressure suit would be required above 40,000' and full pressure above 60,000'.

The flightcrew and skydiver would require oxygen and thermal clothing to protect themselves from arctic temperatures whilst the aircraft is fully depressurised. Due to the thinner air at 40,000 feet the skydiver would descend at a higher fall rate. Ideally any jump at and beyond 40,000 feet would require a pressure suit to protect the skydiver from the freezing temperatures and low atmmopheric pressure.

The record highest skydive was broken in 2012 after standing for over 50 years. The exit altitude was 128,097'.