Answer
$v'_A=3.7\frac{m}{s}$ to the right
$v'_B=2.0\frac{m}{s}$
Work Step by Step
In the y direction
$mv_A=mv_B'+mv'_{Ay}$
$v_A=v_B'+v'_{Ay}$
In the x direction
$mv_B=mv'_{Ax}$
$v_B=v'_{Ax}=3.7\frac{m}{s}$
$\frac{mv_A^2}{2}+\frac{mv_B^2}{2}=\frac{mv_A'^2}{2}+\frac{mv_B'^2}{2}$
$v_A^2+v_B^2=v_A'^2+v_B'^2$
$(v_B'+v'_{Ay})^2+(v'_{Ax})^2=v_A'^2+v_B'^2$
$(v_B')^2+2(v_B')(v'_{Ay})+(v'_{Ay})^2+(v'_{Ax})^2=v_A'^2+v_B'^2$
$2(v_B')(v'_{Ay})=0$
$v'_{Ay}=0$
$v'_A=v'_{Ax}=3.7\frac{m}{s}$