The purpose of the flight was to fly the airplane to the destination airport, where the pilots would commence a Civil Air Patrol, U.S Air Force assigned mission. As the pilots arrived in the area of the destination airport the pilot flying (a certified flight instructor in the left seat) asked the pilot-not-flying (a private pilot in the right seat) if he wanted to practice takeoffs-and-landings. The flight instructor turned over the controls to the private pilot, and he performed a normal landing. The private pilot then set up for a short-field landing. Both pilots reported the airplane touched down "firm" on the main landing gear and as the airplane decelerated it felt as if the airplane had a flat tire. Shortly after, the propeller began to strike the runway. A postaccident examination of the airplane revealed damage to the nose landing gear attachment assembly and substantial damage to the firewall. During postaccident interviews, neither pilot could recall the airspeed during the approach, or the flap configuration. The flight instructor described the landing flare as a "momentary or short flare."