Answer
$2.84m/s$
Work Step by Step
We can determine the required velocity as follows:
$v_{a,2}^2=\frac{2}{m_a}\cdot[\frac{m_av_{a,1}^2}{2}+m_agh]$
We plug in the known values to obtain:
$\implies v_{a,2}^2=\frac{2}{5}\cdot[\frac{5(25)}{2}+5(1.5)(9.81)]$
$\implies v_{a,2}=7.38m/s$
Now according to the law of conservation of momentum
$m_av_{a,2}+m_bv_{b,1}=(m_a+m_b) v$
This simplifies to:
$v=\frac{m_a v_{a,2}}{m_a+m_b}$
We plug in the known values to obtain:
$v=\frac{5(7.38)}{5+8}$
$\implies v=2.84m/s$
