Problem $3.$

Two spherical balls moving with initial velocities $v_A=v_B=10\frac{m}{s}$ collide as shown. The mass of ball $B$ is twice that of ball $A$; that is: $m_B=2m_A.$ If the coefficient of restitution is $e=0\mathrm{.}90,$

Determine the magnitude of the velocities of each ball just after impact, that is$,,(v_A^{\text{'}}{)}_x,(v_A^{\text{'}}{)}_y,(v_B^{\text{'}}{)}_x,(v_B^{\text{'}}{)}_y$ with respect to the $x-y$ coordinate system shown.