A man walks down an inclined plane at 5 m s⁻¹ along a direction 37° below the horizontal and sees rain falling vertically. When he walks up the same incline at the same speed, rain appears at angle θ=tan⁻¹(7/8) with the horizontal. Find the actual speed of rain.
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Question

A man walks down an inclined plane at 5 m s⁻¹ along a direction 37° below the horizontal and sees rain falling vertically. When he walks up the same incline at the same speed, rain appears at angle θ=tan⁻¹(7/8) with the horizontal. Find the actual speed of rain.

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G1 Physics · Accepted Answer

Resolve the man's velocity into horizontal and vertical components using sin37°=3/5 and cos37°=4/5. The first observation fixes the rain horizontal component. Applying the second apparent-angle condition and solving the component equations gives rain speed √32 m s⁻¹. Option B.