Part A

Taking the $x$ axis to be the original direction of motion of ball $A,$ choose the correct equation expressing the conservation of momentum for the components in the $x$ direction.

$0=(m_A{v}_A+m_B{v}_B^{\text{'}})sin{}_B^{\text{'}}$

$m_A{v}_A=m_A{v}_A^{\text{'}}cos{}_A^{\text{'}}-m_B{v}_B^{\text{'}}sin{}_B^{\text{'}}$

$0=m_A{v}_A^{\text{'}}sin{}_A^{\text{'}}-m_B{v}_B^{\text{'}}sin{}_B^{\text{'}}$

$m_A{v}_A=m_A{v}_A^{\text{'}}cos{}_A^{\text{'}}+m_B{v}_B^{\text{'}}cos{}_B^{\text{'}}$

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