Let's consider two students, Student A and Student B, walking toward each other at the same rate. We'll denote their speed as \( v \).
Velocities Relative to a Spot on the Floor
- Both students are walking toward each other at the same speed, \( v \).
- For example, if Student A is moving from left to right at speed \( v \), and Student B is moving from right to left at speed \( v \), their velocities relative to the spot on the floor would be:
- Velocity of Student A: \( +v \)
- Velocity of Student B: \( -v \)
Velocities Relative to Each Other
- To find the velocity of Student A relative to Student B, we consider the formula for relative velocity: \[ v_{A \text{ relative to } B} = v_A - v_B \]
- In this case: \[ v_{A \text{ relative to } B} = v - (-v) = v + v = 2v \]
Summary
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Relative to the floor:
- Student A has a velocity of \( v \).
- Student B has a velocity of \( -v \).
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Relative to each other:
- The velocity of Student A relative to Student B is \( 2v \).
Thus, while both students are moving at the same speed in opposite directions relative to the floor, their closing speed, or relative velocity to each other, is \( 2v \). This means they are getting closer at a rate that is twice their individual walking speed.