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Question

Consider an elastic, head-on collision between

an object of mass m moving at speed v0 and

an object of mass 3 m, initially at rest. After the collision the mass m moves at a

velocity ~v1 and the mass 3 m at velocity of ~v2,

both along the original line of motion. What are the final velocities ~v1 and ~v2?

The sign on each will determine the direction

of the motion.

Answer 1

For an elastic, head on collision, we know (from conservation of energy) that

v₀ = v₂ - v₁

so here v₁ = v₂ - v₀

Conserve momentum, substituting for v₁:

m*v₀ = m*(v₂ - v₀) + 3m*v₂ → → mass m cancels

v₀ = v₂ - v₀ + 3v₂

2v₀ = 4v₂

v₂ = v₀ / 2

You have to choices where this is true, so solve for v₁:

v₁ = v₀/2 - v₀ = -v₀/2

making #6 the correct choice.

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