A hiker walks from the drop-off and initially covers 3000 m, 35° north of west. He then traveled another 5500 m heading to 10° west of north. Finally, he reached his destination by walking 1500 m due north. What is his total displacement?
Scale: 1 cm = 1000 m
Solve this problem using protactor

To solve this problem using a protractor, we'll break it down step by step by drawing the vectors, measuring angles, and then calculating the total displacement vector.

### Step 1: Drawing the vectors
1. **First vector (3000 m, 35° north of west):**
   - Start by drawing the first vector 3 cm long (since 1 cm = 1000 m) at an angle of 35° north of west. This angle means you should draw the vector 35° above the westward direction.
   
2. **Second vector (5500 m, 10° west of north):**
   - From the endpoint of the first vector, draw the second vector 5.5 cm long at an angle of 10° west of north. This angle means you should draw the vector 10° to the left of the northward direction.

3. **Third vector (1500 m due north):**
   - From the endpoint of the second vector, draw the third vector 1.5 cm long directly upward (due north).

### Step 2: Measuring the resultant vector
- After drawing the three vectors, the resultant vector (total displacement) is the straight line from the starting point (origin) to the final endpoint of the third vector.
- Measure the length of this line using your ruler. Convert the length in centimeters to meters (multiply by 1000).

### Step 3: Measuring the angle of the resultant vector
- Use the protractor to measure the angle of this resultant vector relative to a reference direction (typically north or east).

### Example Calculation (Approximate):
1. Draw the first vector, 3 cm at 35° north of west.
2. From the endpoint of this vector, draw the second vector, 5.5 cm at 10° west of north.
3. From the endpoint of this vector, draw the third vector, 1.5 cm due north.
4. Measure the resultant displacement vector length.
   - Suppose the length is approximately 8 cm, then the displacement is 8000 m.
5. Measure the angle using the protractor relative to north (let’s say it’s approximately 25° east of north).

### Step 4: Conclusion
The total displacement would be approximately 8000 m at 25° east of north.

Would you like to ask any more detailed questions or require clarification? Here are some related problems:

1. How do you calculate displacement using the Pythagorean theorem?
2. What is the difference between distance and displacement?
3. How do vector components help in calculating displacement?
4. Can displacement be negative? Explain.
5. What is the significance of using a protractor in vector problems?
6. How do angles affect the resultant displacement in vector addition?
7. How can you determine the direction of the resultant vector without a protractor?
8. How does vector subtraction differ from vector addition?

**Tip:** When drawing vectors, ensure your angles are accurate using the protractor to avoid errors in calculating displacement.

Learn how to calculate total displacement of a hiker using vectors and trigonometry. This problem involves vector addition and trigonometric calculations to determine the resultant displacement. Suitable for students in Grades 10-12.

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