The Russian missiles that tore into a Ukrainian military academy on Tuesday proved so lethal because cadets had barely two minutes to seek safety in a bomb shelter and because debris from explosions then blocked emergency exits, the academy director said Wednesday.

The director, Ihor Matsiuk, said that the strike on the academy, in the eastern city of Poltava, happened as lessons were in session and most of the cadets were in class. Many students in classrooms near the shelter survived, while those farther away suffered a higher toll in dead and wounded, Mr. Matsiuk said at a news conference.

Two of six emergency exits were blocked, he said, while interior corridors that students might have used for escape collapsed.

When the air alarm sounded, “everyone started running to the shelter,” said Andriy, a cadet who was interviewed at a hospital as he visited wounded friends and who asked to be identified only by his first name. He reached the shelter just as there was “a terrible roar and the ground shook,” he said, adding somberly, “I managed to get into the shelter, unlike others.”

Within seven minutes of the alarm’s sounding, the academy had evacuated more than 1,000 people, Mr. Matsiuk said.