Consider a partially elastic collision in which ball $\backslash ($ A $\backslash )$ of mass $\backslash ($ m $\backslash )$ with initial velocity $\backslash ($ v $\backslash )$ collides with stationary ball B $,$ also of mass $\backslash ($ m $\backslash ),$ and in which $\backslash (\backslash$frac$\{1\}\{4\}\backslash )$ of the mechanical energy is dissipated as thermal energy.

Find expression for the final velocitiy of ball A $.$

Hint: Mathematically there are two solutions; however, one of them is physically impossible.

Express your answer in terms of the variable $\backslash ($ v $\backslash ).$

$\backslash [$

$\backslash$left$($v$\_\{\backslash$mathrm$\{$f$\}$ x$\}\backslash$right$)\_\{\backslash$mathrm$\{$A$\}\}=[$

$\backslash ]$

Part B

Find expression for the final velocitiy of ball B $.$

Hint: Mathematically there are two solutions; however, one of them is physically impossible.

Express your answer in terms of the variable $\backslash ($ v $\backslash ).$

$\backslash [$

$\backslash$left$($v$\_\{\backslash$mathrm$\{$f$\}$ x$\}\backslash$right$)\_\{\backslash$mathrm$\{$B$\}\}=$

$\backslash ]$