A $70$ g ball $B$ dropped from a height $h_0=1\mathrm{.}5m$ reaches a height $h_2=0\mathrm{.}25m$ after bouncing twice from identical $210-g$ plates. Plate A rests directly on hard ground, while plate $C$ rests on a foam$-$rubber mat. Determine $($a$)$ the coefficient of restitution between the ball and the plates, $($b$)$ the height $h_1$ of the ball's first bounce.