Answer
$ s_B=71.4mm$
Work Step by Step
According to conservation of linear momentum
$m_A(v_A)_{\circ}+m_B(v_B)_{\circ}=m_Av_A+m_Bv_B$
We plug in the known values to obtain:
$5(0)+30(0)=5(v_A)+30v_B$
This simplifies to:
$v_A=6v_B$
But we know that:
$v_{B/A}=v_B-(-v_A)$
$\implies v_{B/A}=v_B+6v_B=7v_B$
We integrate with respect to time to obtain:
$\implies s_{B/A}=7s_B$
As $s_{B/A}=0.5m$
$\implies s_B=\frac{s_{B/A}}{7}$
$\implies s_B=\frac{0.5}{7}$
$\implies s_B=0.071m=71.4mm$
