Formula Momentum Conservation for the Collision of Two Masses
$$m_1 \, \class{red}{v_1} ~+~ m_2 \, \class{blue}{v_2} ~=~ m_1 \, \class{red}{v'_1} ~+~ m_2 \, \class{blue}{v'_2}$$ $$\class{red}{v_1} ~=~ \class{red}{v'_1} ~+~ \frac{m_2}{m_1} \, \left( \class{blue}{v'_2} ~-~ \class{blue}{v_2} \right)$$ $$\class{blue}{v_2} ~=~ \class{blue}{v'_2} ~-~ \frac{m_1}{m_2} \, \left( \class{red}{v_1} ~-~ \class{red}{v'_1} \right)$$ $$m_1 ~=~ \frac{ \class{blue}{v'_2} ~-~ \class{blue}{v_2} }{ \class{red}{v_1} ~-~ \class{red}{v'_1} } \, m_2 $$ $$m_2 ~=~ \frac{ \class{red}{v_1} ~-~ \class{red}{v'_1} }{ \class{blue}{v'_2} ~-~ \class{blue}{v_2} } \, m_1$$ $$\class{red}{v'_1} ~=~ \class{red}{v_1} ~-~ \frac{m_2}{m_1} \, \left( \class{blue}{v'_2} ~-~ \class{blue}{v_2} \right)$$ $$\class{blue}{v'_2} ~=~ \class{blue}{v_2} ~+~ \frac{m_1}{m_2} \, \left( \class{red}{v_1} ~-~ \class{red}{v'_1} \right)$$
Velocity of the first body (before)
$$ \class{red}{v_1} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity of the first body before the collision with the second body. The first body has the momentum \( p_1 = m_1 \, v_1 \).
Velocity of the second body (before)
$$ \class{blue}{v_2} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity of the second body before the collision with the first body. The second body has the momentum \( p_2 = m_2 \, v_2 \).
Mass of the first body
$$ m_1 $$ Unit $$ \mathrm{kg} $$ Here it is assumed that the mass of the first body remains the same before and after the collision.
Mass of the second body
$$ m_2 $$ Unit $$ \mathrm{kg} $$ Here it is assumed that the mass of the first body remains the same before and after the collision.
Velocity of the first body (after)
$$ \class{red}{v'_1} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity of the first body after the collision with the second body.
Velocity of the second body (after)
$$ \class{blue}{v'_2} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$ Velocity of the second body after the collision with the first body.