A particle of mass 2m is moving to the right in projectile motion.At the top of its trajectory,an explosion breaks the particle into two equal parts.After the explosion,one part falls straight down with no horizontal motion.What is the direction of the motion of the other part just after the explosion?
A)up and to the left
B)stops moving
C)up and to the right
D)straight up
E)down and to the right

Question

Quizplus · Accepted Answer

At the top of the particle's trajectory, its velocity vector is horizontal, going to the right. When the explosion breaks the particle into two parts of equal mass, the momentum in the horizontal direction must be conserved. Therefore, the other part that moves after the explosion must have an equal but opposite horizontal velocity to conserve the momentum. Since the particle was moving to the right before the explosion, the other part must move to the left. However, since the top of the particle's trajectory is the highest point, the other part can only move up or down from that point. Therefore, the other part moves up and to the right (choice C) to conserve both momentum and energy.

A Particle of Mass 2m Is Moving to the Right