$1$: Two balls hang from strings of the same

length. Ball A$,$ with a mass of $4$ kg$,$ is swung back to a point

$0\mathrm{.}8$ m above its equilibrium position. Ball A is released from

rest and swings down and hits ball B$.$ After the collision, ball

A rebounds to a height of $0\mathrm{.}2$ m above its equilibrium position,

and ball B swings up to a height of $0\mathrm{.}05$ m$.$

$($a$)$ How fast is ball A going just before collision?

$($b$)$ Find the mass of ball