Question
Question 3
A runner starts at Point B and runs to point A then to point D and finally stops at point C. The runner's total distance was m. The runner's total displacement was m East.
b-a=4m
A-D=8m
d-c=4m
A runner starts at Point B and runs to point A then to point D and finally stops at point C. The runner's total distance was m. The runner's total displacement was m East.
b-a=4m
A-D=8m
d-c=4m
Answers
GPT-4o mini
Let’s break down the information provided in the problem:
1. **Distance and Displacement**: The total distance run (from Point B to Point A, from A to D, and from D to C) is \( m \). The total displacement (the straight-line distance from Point B to Point C) is \( m \) East.
2. **Distance Relationships**:
- The distance from Point B to Point A is \( b \).
- The distance from Point A to Point D is \( b - 4 \) (from the equation \( b - a = 4 \)).
- The distance from Point D to Point C is \( 4 \).
3. **Distances**:
- From the notation, if \( b \) is the distance from B to A, we have:
- Distance from Point B to A: \( b \)
- Distance from Point A to D: \( b - 4 \)
- Distance from Point D to C: \( 4 \)
Let's find the total distance based on this information:
\[
\text{Total Distance} = \text{BA} + \text{AD} + \text{DC}
\]
Substituting the distances into the equation:
\[
\text{Total Distance} = b + (b - 4) + 4
\]
\[
= b + b - 4 + 4
\]
\[
= 2b
\]
Since we know the total distance is \( m \):
\[
2b = m
\]
From this, we can derive that:
\[
b = \frac{m}{2}
\]
4. **Displacement**:
Since the total displacement is \( m \) East, we can associate the directions with the points defined. The runner's movement creates a resultant vector from Point B to Point C. By considering the distances traveled and their respective directions, we will find that the distance from Point C to Point B equals \( m \) in the East direction.
To summarize:
- \( b = \frac{m}{2} \) (this is the distance BA).
- The other points indicate specific traveled distances.
- We conclude that \( a, c, \) and \( d \) can be defined but might be difficult to connect without further definitions on their locations in relation to each other (e.g., where exactly A, D, and C are in terms of a coordinate system).
If you have any more specific questions or need clarification on any part, feel free to ask!
1. **Distance and Displacement**: The total distance run (from Point B to Point A, from A to D, and from D to C) is \( m \). The total displacement (the straight-line distance from Point B to Point C) is \( m \) East.
2. **Distance Relationships**:
- The distance from Point B to Point A is \( b \).
- The distance from Point A to Point D is \( b - 4 \) (from the equation \( b - a = 4 \)).
- The distance from Point D to Point C is \( 4 \).
3. **Distances**:
- From the notation, if \( b \) is the distance from B to A, we have:
- Distance from Point B to A: \( b \)
- Distance from Point A to D: \( b - 4 \)
- Distance from Point D to C: \( 4 \)
Let's find the total distance based on this information:
\[
\text{Total Distance} = \text{BA} + \text{AD} + \text{DC}
\]
Substituting the distances into the equation:
\[
\text{Total Distance} = b + (b - 4) + 4
\]
\[
= b + b - 4 + 4
\]
\[
= 2b
\]
Since we know the total distance is \( m \):
\[
2b = m
\]
From this, we can derive that:
\[
b = \frac{m}{2}
\]
4. **Displacement**:
Since the total displacement is \( m \) East, we can associate the directions with the points defined. The runner's movement creates a resultant vector from Point B to Point C. By considering the distances traveled and their respective directions, we will find that the distance from Point C to Point B equals \( m \) in the East direction.
To summarize:
- \( b = \frac{m}{2} \) (this is the distance BA).
- The other points indicate specific traveled distances.
- We conclude that \( a, c, \) and \( d \) can be defined but might be difficult to connect without further definitions on their locations in relation to each other (e.g., where exactly A, D, and C are in terms of a coordinate system).
If you have any more specific questions or need clarification on any part, feel free to ask!