Explanation

(d) (a ) Impulsive received by $m$
$\overrightarrow{J} = m({\overrightarrow{v}}_{f} - {\overrightarrow{v}}_{i})$
$= m( - 2\widehat{i} + \widehat{j} - 3\widehat{i} - 2\widehat{j})$
$= m( - 5\widehat{i} - \widehat{j})$
And impulse received by $M$
$= - \overrightarrow{J} = m(5\widehat{i} + \widehat{j})$
(b) $mv = m(5\widehat{i} + \widehat{j})$
Or $v = \frac{m}{M}\left( 5\widehat{i} + \widehat{j} \right) = \frac{1}{13}(5\widehat{i} + \widehat{j})$
(c) $e =$ (relative velocity of separation/relative velocity of approach) in the direction of $- \overrightarrow{J} = 11/17$