We know that the path of a projectile thrown from the ground is a parabola (if w

Question

We know that the path of a projectile thrown from the ground is a parabola (if we ignore air resistance), what would be the subsequent path of the CM of the pieces if the projectile exploded in midair? A shell is fired from level ground so as to hit a target 100 m away. Unlocking the shell explodes prematurely and breaks into two equal pieces. The two pieces land at the same time, and one lands 100 m beyond target. Where does the other piece land?... and is the same result true if they land at different times (with one piece still landing 100 m beyond the target)?

Explanation / Answer

(a) The path of the center of mass of the pieces would be parabolic in nature similar to the path if the projectile had not exploded since no external horizontal force is acting on the system to alter the path of the center of mass.

(b) The center of mass of the system will continue to follow the parabolic trajectory as mentioned above. The other particle will fall 100 meters before the target if the two pieces fall at the same time.

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