Answer:
2 m/s
Explanation:
From the conservation of momentum, the initial momentum of the system must be equal to the final momentum of the system.
Let the 10.00 kg mass be [tex]m_1[/tex] and the 12.0 kg mass be [tex]m_2[/tex]. When they collide and stick, they have a combined mass of [tex]m_1+m_2[/tex].
Momentum is given by [tex]p=mv[/tex]. Set up the following equation:
[tex]\displaystyle m_1v_1+m_2v_2=(m_1+m_2)v_f[/tex], where [tex]v_f[/tex] is the desired final velocity of the masses.
Call the right direction positive. To indicate the 12.0 kg object is travelling left, its velocity should be substitute as -8.00 m/s.
Solving yields:
[tex]10\cdot 14 + 12\cdot (-8)=(10+12)v_f\\\implies v_f=\boxed{2 \text{ m/s}}[/tex]
