Copiapo, Chile (CNN) -- Drilling has begun as part of an effort to reach the 33 miners who have been trapped underground in Chile for more than three weeks, authorities said Tuesday.
The effort to drill through more than 2,300 feet (700 meters) of rock and safely extract the workers could take three to four months, officials said. The hole under way is the excavation hole, where the drill bit will be placed.
The miners have been stuck in the desert copper-and-gold mine since an August 5 cave-in and are surviving on supplies funneled to them from above ground through three bore holes, each about 4 inches in diameter.
A second 25-minute video sent Tuesday by the miners held another round of greetings to their relatives, family members who had seen it told CNN. Copies were to be distributed to the news media Wednesday.
Some relatives emerged from a private screening held in the tents that comprise Camp Hope at the entrance to the mine solemn-faced; others were teary; yet most appeared happy.
All the family members said the miners appeared to be in much better condition, much cleaner and much better organized than they appeared during the first video, which was sent up last Thursday.
Most appeared stripped to the waist and bearded in the first video; some had shaved and were modeling high-tech sportswear -- T-shirts and shorts -- that were sent down to them this week. The video showed the miners with photographs their relatives have sent down to them in recent days.
Some of the miners could be heard playing music in the background. A song from Dominican merengue artist Juan Luis Guerra was one. Over the last few days, rescuers have sent the miners MP3 players and small speakers with a selection of music including Mexican rancheras, Puerto Rican reggaeton and Dominican merengue.
Eighteen-year-old Scarlet Sepulveda came out of the meeting crying. "My dad is fine, he's fine, but I miss him a lot," said the daughter of Mario Sepulveda, who held the camera and narrated Thursday's video. "Of course I miss him."
Cristina Nunez, wife of Claudio Yanez, came out beaming. "They're much better; they're cracking jokes; they have their own things; and they're good," she said. "I was very happy to see them."
Jose Vega, the 70-year-old father of Richard Alex Vega, himself a veteran miner, said of his son, "I was a little worried because I didn't see him much in the video. I think, if they have a problem, they steer clear of the video. But then again, he's a bit like me. He doesn't like cameras too much."
The camera, just two inches wide, fits easily through the 4-inch bore hole, has front and side views and can rotate 360 degrees, said Jim Lozano, a product manager with a Fresno, California-based subsidiary of Aries Industries, Inc. "It's able to get into very small openings," he said.
He said it was designed for use in the water-well industry.
On Tuesday, the miners' menu included tea, herbal infusions, a yogurt-and-cereal shake for breakfast, chicken sandwiches for lunch, kiwi at midafternoon and jam sandwiches for the evening meal. In all, the day's meals contain 2,000 calories. In addition, each man is being urged to drink about five liters of water per day.
Wednesday's menu will include rice and shredded beef or pork, the first hot meal the men will have had since they became trapped nearly a month ago, said Jorge Diaz, a medic involved in the miners' care.
Though the dishes are normally served with beans in Chile, Diaz said they would not be included, so that the men -- who are living in close quarters -- can avoid getting intestinal gas.
Two of the 16 smokers were to get nicotine patches. One of the men reported feeling withdrawal symptoms from not being able to smoke, the other one said he couldn't sleep without having a smoke.
Reading material will include press clips about the rescue effort, copies of the "Condorito" cartoon books that are popular in Latin America, and a self-help book entitled "Tactics for Public Speaking." The book was selected after the miners said they wanted to be able to speak eloquently to the news media when they are rescued.
Meanwhile, a four-person team from NASA is set to arrive in Chile this week to help provide physical and behavioral health support to the miners.
A medical official, a nutritional medic, a psychologist and an engineering expert in logistics from NASA will stay at the mine from Wednesday through Friday to help, Chilean Health Minister Jaime Manalich said.
A group of engineers has said it has a "Plan B" that could halve the time it would take to reach the miners.
Walter Herrera, quality control and risk manager for the Chilean mining company GeoTech, has said his company was bringing a specialized device typically used for boring water holes to the mine. The drill would use one of the three bore holes already made as a pilot and widen the diameter to about 28 inches, which officials have said is wide enough for the miners to be hoisted through.
Chile's mining minister has not ruled out the alternative plan, but has cautioned it might not work. He has also said it might not be put into operation.
CNN's Karl Penhaul and Esprit Smith contributed to this report.