Answer
a) $\sum \vec{p}=+7.5kg.m/s$
b) $\vec{v_{01}}=+3.26m/s$
Work Step by Step
a) The total momentum of the system of 2 carts at that instant is $$\sum \vec{p}=m_1\vec{v_1}+m_2\vec{v_2}$$ $$\sum \vec{p}=2.3(+4.5)+1.5(-1.9)=+7.5kg.m/s$$
b) The principle of conservation of linear momentum states that $$\sum \vec{p}_0=\sum \vec{p}_f=+7.5kg.m/s$$ Therefore, $$m_1\vec{v_{01}}+m_2\vec{v_{02}}=+7.5$$ $$\vec{v_{01}}=\frac{+7.5-m_2\vec{v_{02}}}{m_1}$$
At the start, we have $\vec{v_{02}}=0$. We also have $m_1=2.3kg$ and $m_2=1.5kg$. Therefore, $$\vec{v_{01}}=+3.26m/s$$
