1. **State the problem:** You are rowing south at 9.0 m/s relative to the water, and the river water is flowing south at 1.0 m/s relative to the ground. We need to find your speed relative to a ground-based observer. 2. **Understand the directions:** Both your rowing velocity and the river flow velocity are directed south, which means their velocities add up in the same direction. 3. **Calculate the resultant velocity:** Since both velocities are in the same direction (south), the total velocity relative to the ground is the sum of the two speeds: $$v_{total} = v_{row} + v_{river} = 9.0 + 1.0 = 10.0\ \text{m/s}$$ 4. **Interpretation:** You are moving south at 10.0 m/s relative to the ground. **Final answer:** You are going at a speed of **10.0 m/s south** relative to a ground-based observer.