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 collisions, 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?

Engineering

Physics

Collision

Momentum and Energy Conservation for System of Particles

Summation of Vectors

Question

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 collisions, 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?

Each piece moves with speed ν/2.

Each piece moves with speed greater than ν/2.

Each piece moves with speed ν.

One of the pieces moves with speed v, the other moves with speed less than ν.

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mv = mv' cos θ + mv' cos θ

$v^{'} = \frac{v}{2 cosθ}$

$v^{'} > \frac{v}{2}$ .