Answer
$0.375m/s$
$105000N$
Work Step by Step
According to the law of conservation of linear momentum
$m_av_{a,1}+m_bv_{b,1}=m_av_{a,2}+m_b v_{b,2}$
This can be rearranged as:
$v_{a,2}=\frac{m_av_{a,1}+m_b v_{b,1}-m_b v_{b,2}}{m_a}$
We plug in the known values to obtain:
$v_{a,2}=0.375m/s$
Now the required force can be determined as
$m_bv_{b,1} \int ^{0.5}_{0} Fdt=m_b v_{b,2}$
$\implies m_b v_{b,1}(0.5)F=m_b v_{b,2}$
$\implies F=\frac{m_b(v_{b,2}-v_{b,1})}{0.5}$
We plug in the known values to obtain:
$F=105000N$
