A one kilogram rocket is launched into the air at a 45o angle. After traveling 100 m, when its speed was 50 m/s, it breaks into four pieces. A 500 gram piece continues along the original line of travel at a speed of 35 m/s, a 100 gram piece goes directly backward with a speed of 20 m/s, and a 200 gram piece flies straight up with a speed of 10 m/s.
Find what happened to the fourth piece? (What direction did it travel, and at what speed?)