A boat travels across a river whose water flows from left to right at $4.0\,\text{m s}^{-1}$. In still water, the boat has a speed of $6.0\,\text{m s}^{-1}$. The boat is aimed at an angle $\theta$ to a line that is perpendicular to the river banks. The combined velocity $v$ of the boat points in a direction perpendicular to the river banks. Determine the values of $\theta$ and $v$.
- A$\theta = 42^\circ$, $v = 4.5\,\text{m s}^{-1}$
- B$\theta = 42^\circ$, $v = 7.2\,\text{m s}^{-1}$
- C$\theta = 48^\circ$, $v = 4.5\,\text{m s}^{-1}$
- D$\theta = 48^\circ$, $v = 7.2\,\text{m s}^{-1}$