Draw displacement vectors along the route from the West Philippine Sea to Manila. You should be able to trace the route with several displacement vectors connected head-to-tail. You may use as many vectors as needed. For each displacement vector, draw the x- and y-components. Feel free to use different colors for each component in each vector. Use the scale on the map or add gridlines so that the vector components are drawn to scale. Estimate the distance and displacement traveled by your sailboat. Lastly, draw the path of your sailboat if the wind and sea currents (i.e. y-component of each displacement vector) are not present. Given 200km

To complete the task, let's break it down into clear steps and visualize the journey from the West Philippine Sea to Manila. Since this is a conceptual drawing task, I'll describe how you can proceed, including details about the displacement vectors and how to analyze the components:

### 1. **Set up the Map and Route**
   - Imagine the West Philippine Sea (off the coast of the Philippines) and Manila. The route follows a curved or diagonal path since they aren’t directly aligned.
   - Place gridlines on the map (for scale) or use an existing scale from the map to estimate distances. Assume 1 cm on the map = 50 km for the sake of this exercise.

### 2. **Draw the Displacement Vectors**
   - Begin from the West Philippine Sea, plotting the first point.
   - Draw the path of your sailboat using a series of connected **displacement vectors**. A displacement vector starts from one point and ends at the next point on the route.

   - **For example:**
     - Draw the first vector pointing eastward (from the West Philippine Sea towards Luzon Island).
     - The second vector would then point slightly southeast towards Manila.

### 3. **Draw the x- and y-Components of Each Vector**
   For each vector:
   - The **x-component** (horizontal) represents the east-west direction.
     - Use a color like red for the x-component.
   - The **y-component** (vertical) represents the north-south direction.
     - Use a color like blue for the y-component.

   - **For each vector:**
     - Break down the vector into its x- and y-components by drawing a horizontal line from the tail of the vector to the x-axis, and a vertical line from the head of the vector to the y-axis. These two components form a right triangle with the vector as the hypotenuse.
     - Make sure the lengths of these components are proportional to the actual distance.

### 4. **Estimate Total Distance and Displacement**
   - Total **distance traveled** by the boat is the sum of the lengths of all the vectors.
   - **Displacement** is the straight-line distance from the initial point (West Philippine Sea) to the final point (Manila). Displacement is the magnitude of the resultant vector, obtained by adding all the individual displacement vectors.

   You can use Pythagorean theorem to calculate this final displacement.

### 5. **Draw the Path Without Currents (No Y-Component)**
   - If there are no sea currents or wind affecting the north-south direction, you would only have the **x-component** for each displacement vector.
   - The path would become a straight horizontal line, moving directly eastward toward Manila, ignoring any drift north or south.

### Example (Simplified for Estimation):
   - First vector: 150 km at 30° south of east.
     - x-component = \( 150 \cos(30°) = 129.9 \, \text{km} \)
     - y-component = \( 150 \sin(30°) = 75 \, \text{km} \)
   
   - Second vector: 50 km eastward (no y-component).
     - x-component = 50 km.
     - y-component = 0 km.

   Total distance traveled = 150 km + 50 km = 200 km.
   Total displacement (hypotenuse of the total vectors): can be calculated using vector addition.

---

Would you like to proceed with a drawing based on this approach, or need further elaboration on any of these steps?

Here are some related questions:
1. How do you determine the angle between the displacement vectors and axes?
2. What tools can be used to simplify vector addition in real-world navigation?
3. How does sea current influence the total distance and displacement?
4. What differences arise in calculating displacement if your path is circular rather than straight?
5. How can the Pythagorean theorem help in calculating the resultant displacement?

**Tip:** Always break complex movements into simpler vectors to ease the calculations of total displacement.

Draw displacement vectors along the route from the West Philippine Sea to Manila. You should be able to trace the route with several displacement vectors connected head-to-tail. You may use as many vectors as needed. For each displacement vector, draw the x- and y-components. Feel free to use different colors for each component in each vector. Use the scale on the map or add gridlines so that the vector components are drawn to scale. Estimate the distance and displacement traveled by your sailboat. Lastly, draw the path of your sailboat if the wind and sea currents (i.e. y-component of each displacement vector) are not present. Given 200km.

Learn how to draw displacement vectors from the West Philippine Sea to Manila. Break down each vector into x- and y-components and estimate total distance and displacement traveled. Understand how wind and sea currents influence the journey, with step-by-step vector analysis. Suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation