1. **State the problem:** You swim at 1.0 m/s north relative to the water, and the river flows at 0.30 m/s east. We want to find your speed relative to a ground-based observer. 2. **Identify the vectors:** Your velocity relative to water is \( \vec{v}_s = 0\hat{i} + 1.0\hat{j} \) m/s (north is along the y-axis). The river's velocity relative to ground is \( \vec{v}_r = 0.30\hat{i} + 0\hat{j} \) m/s (east is along the x-axis). 3. **Calculate your velocity relative to ground:** $$\vec{v}_g = \vec{v}_r + \vec{v}_s = 0.30\hat{i} + 1.0\hat{j}$$ 4. **Find the magnitude of your velocity relative to ground:** $$|\vec{v}_g| = \sqrt{(0.30)^2 + (1.0)^2} = \sqrt{0.09 + 1.0} = \sqrt{1.09} \approx 1.044\, \text{m/s}$$ 5. **Interpretation:** You are moving at approximately 1.044 m/s relative to the ground, in a direction northeast. **Final answer:** Your speed relative to the ground is approximately $1.04$ m/s.