A cannonball is on track to hit a distant target when, at the top of its flight, it unexpectedly explodes into two pieces that fly out horizontally. You find one piece of the cannonball, and you know the target location. What physics principle would you apply to find the other piece? Explain.
When you fire a cannonball, it's path is a parabola (assuming we can ignore air resistance).. To be accurate, we should say the centre of mass of the cannonball follows a parabolic path.
But if the cannonball splits into a number of pieces, the centre of mass of all the pieces STILL moves along the same parabolic path - even though the individual pieces follow different paths.
Suppose the cannonball splits into 2 equal mass pieces which land at 2 different places. The centre of mass of these 2 pieces is midway along the line joining the piece - this midpoint is where the cannonball would have landed if it hadn't split in 2