https://file.aiquickdraw.com/mathbot/file/1730180681196w6g2yhe4.jpg

Let’s break down each part of the problem for Path C:

1. **Part 1**: You've already given the formula for resultant displacement as:
   \[
   \text{Resultant Displacement} = \sqrt{x^2 + y^2}
   \]
   where \( x \) and \( y \) are the horizontal and vertical components of displacement.

2. **Part 2**: To find the total distance traveled along Path C, observe the path in the grid and count the number of blocks covered. Multiply the total blocks by the distance of a single block, which is 93.0 m.

3. **Part 3**: 
   - **Magnitude**: This will be the resultant displacement from Part 1. Determine \( x \) and \( y \) based on the net movement horizontally and vertically (i.e., the difference in the start and finish positions).
   - **Direction**: Calculate the direction using:
     \[
     \theta = \arctan\left(\frac{y}{x}\right)
     \]
     where \( \theta \) is the angle north of east.

Let me know if you want further details on any part, or if you'd like to solve any components together!

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### Follow-up Questions:

1. How do we determine the values for \( x \) and \( y \) based on the path?
2. Why is the total distance different from the resultant displacement?
3. Can we use Pythagorean Theorem for displacement in any path configuration?
4. What other trigonometric functions can we use to find direction, if any?
5. How does displacement change if the path is circular?

### Tip:
For calculating the direction, ensure that \( x \) and \( y \) are taken with correct signs (positive or negative) based on the direction of movement.

Find the following for path C in the figure. The distance of a city block is 93.0 m.
1. Give the equation to determine the magnitude of the total displacement in terms of the horizontal component (x) and vertical component (y).
2. Find the total distance traveled.
3. Find the magnitude and direction of the displacement from start to finish.

Learn how to determine the magnitude of displacement, total distance traveled, and the direction for path C in a city grid, where each block measures 93.0 m. This tutorial includes key formulas such as the Pythagorean Theorem for displacement and trigonometric functions for angle calculation, suitable for high school students.

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