Answer
$v = (10\hat{i} +15\hat{j})~m/s$
Work Step by Step
We can find the x-component of the final velocity:
$Mv_x +M(-5.0~m/s)= M(15~m/s)+M(-10~m/s)$
$v_x = (15~m/s)+(-10~m/s)+(5.0~m/s)$
$v_x = 10~m/s$
We can find the y-component of the final velocity:
$Mv_y +M(20~m/s)= M(30~m/s)+M(5.0~m/s)$
$v_y = (30~m/s)+(5.0~m/s)+(-20~m/s)$
$v_y = 15~m/s$
We can express the final velocity of B:
$v = (10\hat{i} +15\hat{j})~m/s$
