Suppose you are in a sailboat in the west philippine sea going to manila. Your captain has already mapped your route on the map and your job as the navigator is to draw the displacement vectors along the route so that you can sail. If wind and sea currents are not present, the sailboat will travel eastward mantaining a constant speed. But since there are mostly southward wind and sea currents, you are able to adjust the sail and follow.

Draw a 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.
For each displacement vector, draw tge x- and y-components. Use different colors for each component in vectors. 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.

To help you visualize the displacement vectors and components, let's break down the task step-by-step:

### **Steps to Draw Displacement Vectors and Components:**

1. **Route Mapping:**
   - Your route from the West Philippine Sea to Manila will be represented on a map. We assume it consists of several segments where each segment represents a displacement vector.

2. **Displacement Vectors:**
   - Draw vectors along the route, connected head-to-tail, showing the direction and magnitude of your sailboat’s movement.
   - Vectors should represent the actual direction influenced by wind and sea currents, which is generally eastward with a southward adjustment due to the wind and sea currents.

3. **Components of Vectors:**
   - For each displacement vector, draw the x-component (eastward direction) and y-component (southward direction).
   - Use different colors for each component: e.g., red for x-components and blue for y-components.

4. **Scaling and Gridlines:**
   - Add gridlines or use the scale on the map to ensure the vectors and components are accurately represented to scale. You may use a standard scale such as 1 cm = 10 km, depending on the map's scale.

5. **Distance and Displacement:**
   - Calculate the total distance traveled by measuring each vector segment and summing their lengths.
   - Displacement is the straight-line vector from the start point (West Philippine Sea) to the endpoint (Manila).

6. **Path Without Wind and Currents:**
   - Draw a hypothetical path assuming only the x-components (eastward movement) are present. This will represent the path of the sailboat in the absence of wind and sea currents.

### **Estimating Distance and Displacement:**

To estimate the distance and displacement:
- Use the scale to measure the length of each displacement vector.
- Apply trigonometric functions to find the magnitude of each component if exact vector angles are given.
- Sum up the distances of each segment for total distance.
- Use the Pythagorean theorem for total displacement: \( \text{Displacement} = \sqrt{(\text{Total x-component})^2 + (\text{Total y-component})^2} \).

### **Example Calculation:**
Suppose the following displacements:
- Vector 1: 50 km east, 10 km south.
- Vector 2: 40 km east, 15 km south.
- Vector 3: 60 km east, 20 km south.

Calculations:
- Total x-component: \( 50 + 40 + 60 = 150 \) km east.
- Total y-component: \( 10 + 15 + 20 = 45 \) km south.
- Total displacement: \( \sqrt{(150)^2 + (45)^2} \approx 156.6 \) km.

### **Visual Representation:**
Currently, I can guide you through how to draw these vectors on paper, or you can upload a photo of your route map, and I can assist you further in analyzing it!

Would you like further details or have any questions? Here are some follow-up tasks and tips:

1. How to determine the exact angles of each displacement vector on the map?
2. How to adjust vector lengths based on map scaling?
3. How to accurately represent southward adjustments due to wind and sea currents?
4. Calculating the impact of southward components on the travel time.
5. Analyzing how changes in wind direction would affect the route.

**Tip:** Always label your vectors clearly, including directions and magnitudes, to avoid confusion during navigation.

Suppose you are in a sailboat in the West Philippine Sea going to Manila. Your captain has already mapped your route on the map and your job as the navigator is to draw the displacement vectors along the route so that you can sail. If wind and sea currents are not present, the sailboat will travel eastward maintaining a constant speed. But since there are mostly southward wind and sea currents, you are able to adjust the sail and follow.

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. For each displacement vector, draw the x- and y-components. Use different colors for each component in vectors. 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.

Learn how to draw displacement vectors and their components along a route from the West Philippine Sea to Manila. This problem involves vector components, estimating distance and displacement using trigonometric functions and the Pythagorean theorem. Suitable for students in Grades 10-12.

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