On April $15,1999,$ a South Korean cargo plane crashed due to a confusion over units. After takeoff, the first officer was instructed by the Shanghai tower to climb to $1500m$ and maintain that altitude. The captain, after reaching $1450m,$ twice asked the first officer a what altitude they should fly. Each time, the first officer replied incorrectly that they were to fly at $1500ft.$ The captain started a steep descent; the plane could not recover from the dive and crashed. How far above the correct altitude were they when they started the rapid descent? $($Aircraft altitudes are given in feet throughout the world except in China, Mongolia, and the former Soviet states, where meters are used.$)$