1. **Problem statement:** A tourist travels north 10 km in 2 hours, rests 30 minutes, then travels east 8 km in 1 hour. We need to find: a) The average velocity vector for the whole trip. b) The average speed (scalar) for the whole trip. 2. **Key formulas:** - Average velocity vector $\vec{v}_{avg} = \frac{\vec{d}_{total}}{t_{total}}$ where $\vec{d}_{total}$ is total displacement vector and $t_{total}$ is total time. - Average speed $= \frac{\text{total distance}}{t_{total}}$. 3. **Calculate total displacement vector:** - North displacement: $10$ km in $\hat{j}$ direction. - East displacement: $8$ km in $\hat{i}$ direction. So, $\vec{d}_{total} = 8\hat{i} + 10\hat{j}$ km. 4. **Calculate total time:** - Travel north: 2 hours - Rest: 0.5 hours - Travel east: 1 hour Total time $t_{total} = 2 + 0.5 + 1 = 3.5$ hours. 5. **Calculate average velocity vector:** $$\vec{v}_{avg} = \frac{8\hat{i} + 10\hat{j}}{3.5} = \frac{8}{3.5}\hat{i} + \frac{10}{3.5}\hat{j} = \frac{\cancel{8}}{\cancel{3.5}}\hat{i} + \frac{\cancel{10}}{\cancel{3.5}}\hat{j} = 2.29\hat{i} + 2.86\hat{j} \text{ km/h}$$ 6. **Calculate total distance traveled:** Distance north $= 10$ km Distance east $= 8$ km Total distance $= 10 + 8 = 18$ km 7. **Calculate average speed:** $$\text{Average speed} = \frac{18}{3.5} = \frac{\cancel{18}}{\cancel{3.5}} = 5.14 \text{ km/h}$$ **Final answers:** - a) Average velocity vector $= 2.29\hat{i} + 2.86\hat{j}$ km/h - b) Average speed $= 5.14$ km/h