The solo student pilot reported that, during landing, on short final, he saw a helicopter on the runway and initiated a go around. During the go-around, the helicopter took off and he believed that it was "heading directly for [the airplane]", which "made [him] very anxious". The helicopter departed without further incident and the airplane re-entered the traffic pattern to land. During his second attempt to land, immediately after touchdown, the airplane's nose landing gear touched down hard and the airplane bounced "3 to 4 times.". When the airplane touchdown again, the nosewheel tire blew. The flight instructor added that, while watching from the fuel farm, the student pilot did not flare the airplane. The Federal Aviation Administration (FAA) inspector reported that the airplane sustained substantial damage to the engine mount and truss. The FAA inspector reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.