Answer
$v_f = 645\hat{i}+132\hat{j}$
Work Step by Step
We find the sum of the initial momentums:
$P_0=32(580)\hat{i}+16(870)cos27\hat{i}+16(870)sin27\hat{j}$
$P_0=30,962\hat{i}+6319\hat{j}$
We divide this by the total final mass to find:
$v_f = 645\hat{i}+132\hat{j}$
