Classical Mechanics - Conservation of Momentum

A particle of mass m is moving along the x-axis with speed v when it collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest, and the second particle has split into two equal-mass pieces that move at equal angles θ  0 with the x-axis, as shown in the figure. Which of the following statements correctly describes the speeds of the two pieces?

A. Each piece moves with speed v
B. One of the pieces moves with speed v, the other moves with speed less than v.
C. Each piece moves with speed v/2
D. One of the pieces moves with speed v/2, the other moves with speed greater than v/2.
E. Each piece moves with speed greater than v/2

(GR0177 #55)

Solution:

Conservation of momentum:



Answer: E