relative motion (rain & man)

Question

Rain falls vertically with speed 12 m/s. A person runs east at 4.36 m/s and observes the rain at 20° from vertical. What is the horizontal velocity component of the rain relative to ground?

RankGuru · Accepted Answer

1. **Analyze Reference Frames**: 
   - The problem states rain falls **vertically** relative to the ground frame.
2. **Ground Frame Components**: By definition, horizontal component $= 0$ m/s; vertical component $= 12$ m/s downward.
3. **Relative Frame Check**: Relative to the runner moving East at $u$, the rain has a relative horizontal velocity of $-u$ (West).
   - Apparent angle $	heta$ from vertical: $	an 	heta = \frac{u}{v_{rain}} = \frac{4.36}{12} \approx 0.363$.
   - $\arctan(0.363) \approx 19.95^\circ$ (approx $20^\circ$). Information is consistent.
4. **Deduction**: The question specifically asks for the horizontal component **relative to the ground**.
5. **Conclusion**: Since the rain falls vertically in the ground frame, its horizontal velocity component is **$0$ m/s**.

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relative motion (rain & man)

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