$13\mathrm{.}185$ Ball $B$ is hanging from an inextensible cord. An identical ball $A$ is released from rest when it is just touching the cord and drops through the vertical distance $h_A=8in.$ before striking ball $B.$ Assuming $e=0\mathrm{.}9$ and no friction, determine the resulting maximum vertical displacement $h_B$ of the ball $B.$

Fig. P$13\mathrm{.}18$

$($ can the answer be found without using any trig, please show all steps to sloving this problem$)$