A 10.0 kg shell is fired vertically upward. At its max height of 500.0 m, it explodes into 3 pieces. It's noticed that all 3 pieces land simultaneously on the (level) ground. A 5.0 kg chunk lands 25.0 m away, 45 degrees due northeast from the launch site. A 2.0 kg piece lands 35.0 m, 30 degrees south of east from the launch site. Where does the third piece land?