A small private jet crashed in woods and burned Sunday afternoon near a small airport in rural Virginia, killing all five people aboard, police said.The twin-engine IAI Astra 1125 went down amid trees along an airport road in Hot Springs, a community in the shadow of the Allegheny Mountains, killing the pilot and three other adults along with a child, Virginia State Police said in a statement. Video above: Members of the Amish community were victims of a plane crashPolice and other emergency responders converged on the site in Bath County after the crash occurred about 3 p.m.A state police spokesman told The Associated Press that the plane caught fire on impact. Investigators were working to confirm the origin of the flight and where it was flying to, Sgt. Rick Garletts said by email Sunday evening. "Small crash site, everything is burnt, meaning the tail numbers are unidentifiable," Garletts said, adding state police were working with the Federal Aviation Administration and the National Transportation Safety Board to try to identify the flight details and the occupants.An FAA statement gave no preliminary information on the circumstances of the crash and said that the agency and the NTSB will investigate. Hot Springs is located about 165 miles (265 kilometers) west of the Virginia capital city, Richmond.Local reports showed what appeared to be plumes of white smoke rising from an impact site. The airport was closed in the aftermath of the crash.Police said they had no further details and planned no further updates Sunday evening as the investigation continues.