Answer
$\vec{v}=4.4\hat{i}+3.0\hat{j}$
Work Step by Step
We know that momentum is conserved. We assume the astronaut is initially at rest. We first find the final speed of the astronaut:
$\vec{v}=-.85cos(20)\hat{i}-.85sin(20)\hat{j}$
$\vec{v}=-.8\hat{i}-.29\hat{j}$
Thus, we use conservation of momentum:
$(5.8)v_3 +(-.8\hat{i}-.29\hat{j})(60)+1.6(14)\hat{i}=0$
$\vec{v}=4.4\hat{i}+3.0\hat{j}$
