Two pucks $(m_A=0\mathrm{.}500kg$ and $($:$m_b=0\mathrm{.}300(kg)\}$ collide elastically on a frictionless air$-$hockey table. Puck A has an initial velocity of $4\mathrm{.}00\frac{m}{s}$ in the positive $x-$direction and a final velocity of $2\mathrm{.}00\frac{m}{s}$ in an unknown direction $.$ Puck $B$ is initially at rest.

$($a$)$ Find the final speed of puck B$.$

$($b$)$ Find $.$

$($c$)$ Find $.$