Question

A 2kg yellow cart rolls right with velocity of 6 m/s and collides with a 3kg orange cart moving right with velocity of 1 m/s. After collision, the orange cart moves right with velocity of 5 m/s. What is speed and direction of of the yellow cart?

Answer 1

Law of conservation of moment:

$m_y\vec{v}_{y1}+m_o\vec{v}_{o1}=m_y\vec{v}_{y2}+m_o\vec{v}_{o2}\\ m_y{v}_{y1}+m_o{v}_{o1}=m_y{v}_{y2}+m_o{v}_{o2}\\ {v}_{o2} = \frac{m_y{v}_{y1}+m_o{v}_{o1}}{m_o} = \frac{2\cdot6+3\cdot1}{3} = 5\,m/s$

So, the yellow cart moves right with velocity of 5 m/s