Which is exactly what we got before. This will become more clear soon when we discuss the center of mass. Compare the calculation above to the one done at the beginning of Lecture 3 and you'll begin to see why the Conservation Laws are so powerful. Total momentum is conserved if there are no external forces. Conservative forces give energy back.
Total energy is conserved if there are no non-conservative forces.
Conservation Laws allow you to calculate motional properties without detailed information about the forces causing the motion We will introduce the concept of the Center of Mass and we'll use it to analyze the pole vault and the high jump.