Momentum conservation in a completely inelastic collision (7-18)

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Question

Velocities of objects A and B before they undergo a completely inelastic collision (in which they stick together)

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Review

When an object of mass $m_A$ and velocity $\vec{v}_{Ai}$ undergoes an inelastic collision with a second object of mass $m_B$ and velocity $\vec{v}_{Bi}$ , we can regard what remains after the collision as a single object of mass $m_A + m_B$ . Momentum conservation then gives us an equation for the velocity $\vec{v}_f$ of this combined object just after the collision: