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A particle of mass m moving along the x-axis with speed v strikes a stationary particle of mass 2m. After the collision the first particle stops, and the 2m particle breaks into two equal pieces that fly off at equal angles theta > 0 on either side of the x-axis. Which statement about the speeds of the two pieces is correct?

1. Each piece moves with speed v
2. One of the pieces moves with speed v, the other moves with speed less than v
3. Each piece moves with speed v/2
4. Each piece moves with speed greater than v/2

Correct answer: Each piece moves with speed greater than v/2

Solution

Momentum along x gives 2*m*v_piece*cos(theta) = m*v, so v_piece = v/(2*cos(theta)); since cos(theta) < 1 for theta > 0, v_piece > v/2.

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