On a frictionless horizontal table, puck A $($with mass $0\mathrm{.}20$ kg $)$ is moving to the right towards puck B $($with mass $0\mathrm{.}40$ kg $),$ which is initially at rest. After the collision, puck A has velocity $0\mathrm{.}5$m$/$s to the left, and puck B has velocity $4\mathrm{.}0$m$/$s to the right. Calculate:

a$)$ the velocity of puck A just before collision. $(5$ pts$)$

b$)$ the fraction of the initial kinetic energy lost during the collision. $(5$ pts$)$