A stationary man must hold his umbrella at 30° to the vertical to avoid rain. When he runs at 10 km h⁻¹, rain falls vertically on his head. The speed of rain relative to the moving man is:
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Question

A stationary man must hold his umbrella at 30° to the vertical to avoid rain. When he runs at 10 km h⁻¹, rain falls vertically on his head. The speed of rain relative to the moving man is:

G1 Physics · Accepted Answer

When the man runs at 10 km h⁻¹ and apparent rain is vertical, the rain's horizontal component is 10 km h⁻¹. For the stationary man, tan30°=horizontal/vertical=10/vᵧ, so vᵧ=10√3 km h⁻¹. Relative speed while running is purely vertical =10√3 km h⁻¹. Option B.