It’s Dante's first day of school at South and he is learning to navigate the hallways. Dante is in the East wing and walks a distance of 22.8 meters eastward followed by another eastward walk of 38.4 meters.

What is the magnitude of Dante's resultant displacement?

Resultant magnitude

meters

Attempts: 0
What is the magnitude of Dante's resultant displacement in a situation in which the 38.4 m walk is in the westward direction, opposite the 22.8 m walk? (Enter a + value.)

Resultant magnitude

meters



Let’s break down the two cases step-by-step to find Dante's **resultant displacement** in each scenario.

---

### **Case 1: Both Displacements are Eastward**

- First displacement: \(22.8 \, \text{m} \, \text{east}\)
- Second displacement: \(38.4 \, \text{m} \, \text{east}\)

Since both displacements are in the **same direction**, we can **add them directly**:  
\[
\text{Resultant displacement} = 22.8 \, \text{m} + 38.4 \, \text{m} = 61.2 \, \text{m}
\]

---

### **Case 2: Opposite Directions (One Eastward, One Westward)**

- First displacement: \(22.8 \, \text{m} \, \text{east}\)
- Second displacement: \(38.4 \, \text{m} \, \text{west}\)

Since these displacements are in **opposite directions**, we subtract the smaller value from the larger one and keep the direction of the larger displacement:  
\[
\text{Resultant displacement} = |38.4 \, \text{m} - 22.8 \, \text{m}| = 15.6 \, \text{m}
\]

---

### **Final Answers**

1. **Case 1**: \(61.2 \, \text{m}\)  
2. **Case 2**: \(15.6 \, \text{m}\)

Both results are positive, as required. 

---

Do you have any further questions? Would you like me to explain any step in more detail?

---

Here are 5 related questions to expand your understanding:
1. What is the difference between displacement and distance?
2. How would the direction of displacement change if the second walk was northward?
3. How do you represent displacement vectors graphically?
4. What happens to the magnitude of displacement when the paths are not straight lines?
5. How is displacement used in physics to calculate velocity?

**Tip:** Always pay attention to direction in displacement problems—it’s crucial when dealing with vectors!

It’s Dante's first day of school at South and he is learning to navigate the hallways. Dante is in the East wing and walks a distance of 22.8 meters eastward followed by another eastward walk of 38.4 meters. What is the magnitude of Dante's resultant displacement? What is the magnitude of Dante's resultant displacement in a situation in which the 38.4 m walk is in the westward direction, opposite the 22.8 m walk? (Enter a + value.)

Learn how to calculate the resultant displacement of Dante's walk when he moves 22.8 meters eastward followed by another 38.4 meters, both in the same direction and in opposite directions. This problem focuses on vector addition principles and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation