Let's break down the girl's journey step by step:

Part 1: Magnitude of the Resultant Displacement

The girl travels:

• 3 blocks west,
• 8 blocks north,
• 6 blocks east.

To calculate the resultant displacement, we treat the girl's movement as a vector journey:

1. The westward and eastward movements are in opposite directions, so they partially cancel each other out:

   • Net horizontal displacement = $6 - 3 = 3$ blocks east.

2. The northward movement is not canceled out:

   • Net vertical displacement = 8 blocks north.

Now, the resultant displacement is the straight-line distance from the starting point to the ending point. This is found using the Pythagorean theorem: $\text{Resultant displacement} = \sqrt{(3)^2 + (8)^2} = \sqrt{9 + 64} = \sqrt{73} \approx 8.54 \, \text{blocks}.$

Part 2: Direction of the Resultant Displacement

The direction of the resultant displacement is measured from due east, counterclockwise, as the angle $\theta$. This angle is found using the tangent function: $\tan(\theta) = \frac{\text{vertical displacement}}{\text{horizontal displacement}} = \frac{8}{3}.$

Now, calculate $\theta$: $\theta = \tan^{-1}\left(\frac{8}{3}\right) \approx 69.44^\circ.$

Part 3: Total Distance Traveled

The total distance she travels is the sum of all the distances covered: $\text{Total distance} = 3 \, \text{blocks} \, (\text{west}) + 8 \, \text{blocks} \, (\text{north}) + 6 \, \text{blocks} \, (\text{east}) = 17 \, \text{blocks}.$

Final Answers:

1. Magnitude of the resultant displacement = $8.54 \, \text{blocks}$.
2. Direction of the resultant displacement = $69.44^\circ$ counterclockwise from due east.
3. Total distance traveled = $17 \, \text{blocks}$.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What if she had traveled 4 blocks south after the eastward leg—what would her new resultant displacement be?
2. How does the direction change if the girl travels 5 blocks west and 8 blocks north instead?
3. Can you derive the equation for the magnitude of displacement for any path?
4. If the girl made the trip twice, what would be her total distance traveled?
5. What if she started from a different point—how would you calculate the new direction?

Tip: Always break down movements into horizontal and vertical components when dealing with vector displacement!