The vector \(\textbf{i}\) represents 1 mile per hour east, and the vector \(\textbf{j}\) represents 1 mile per hour north. According to her GPS, at a particular instant, Tia is biking \(30^\circ\) west of north at 16 miles per hour. One of the following vectors represents Tia's velocity, in miles per hour, at that instant. Which one?

\(-8\textbf{i} -8\sqrt{3}\textbf{j} \)

\(-8\textbf{i} +8\sqrt{3}\textbf{j} \)

\(8\textbf{i} +8\sqrt{3}\textbf{j} \)

\(8\sqrt{3}\textbf{i}-8\textbf{j} \)

\(8\sqrt{3}\textbf{i}+8\textbf{j} \)