Relative Velocity

Question

Two trains are moving in opposite directions with velocities 60 km/h and 40 km/h respectively. A bird is flying at 80 km/h in the same direction as the faster train. What is the relative velocity of the bird with respect to the faster train?

RankGuru · Accepted Answer

1. **Vector Notation**: Let the direction of the faster train (Train A) be positive ($+X$).
   - $\vec{v}_A = +60$ km/h.
   - Bird's velocity $\vec{v}_B = +80$ km/h (same direction).
2. **Relative Velocity Rule**: The velocity of object B relative to A is $\vec{v}_{BA} = \vec{v}_B - \vec{v}_A$.
3. **Substitution**:
   - $v_{BA} = 80 - 60 = 20$ km/h.
4. **Conclusion**: To a passenger on the faster train, the bird appears to be moving forward at 20 km/h.
5. **Note**: The velocity of the second train (40 km/h) is irrelevant to this specific question.

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