Answer:
[tex]\vec{v}_1 = -\frac{\vec{v}_2m_2}{m_1}[/tex]
Explanation:
The center of mass of the system (two girls) is constant, as the velocity of the center of mass of the system is also constant.
[tex]\vec{v}_{cm} = \frac{m_1\vec{v}_1 + m_2\vec{v}_2}{m_1 + m_2}[/tex]
The initial velocity of the system is zero, since both girls are at rest. So the velocity of the total system at any point should be zero as well.
[tex]0 = \frac{m_1\vec{v}_1 + m_2\vec{v}_2}{m_1 + m_2}\\\vec{v}_1 = -\frac{\vec{v}_2m_2}{m_1}[/tex]
This is true, because there is no friction between the girls and the ground. Otherwise, the velocity of the center of mass wouldn't be constant.
