To a man walking at 2 km h⁻¹, rain appears vertical. When he walks at 4 km h⁻¹ in the same direction, rain appears at 45° to the horizontal. The true rain velocity is:
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To a man walking at 2 km h⁻¹, rain appears vertical. When he walks at 4 km h⁻¹ in the same direction, rain appears at 45° to the horizontal. The true rain velocity is:

G1 Physics · Accepted Answer

Let horizontal and vertical components of actual rain velocity be vₓ and vᵧ. When the man moves at 2 km h⁻¹ and rain appears vertical: vₓ-2=0 ⇒ vₓ=2 km h⁻¹. When he moves at 4 km h⁻¹, relative horizontal component has magnitude 2 km h⁻¹. Since apparent angle is 45°: |vᵧ| = 2 km h⁻¹. Thus rain speed: v = √(2²+2²)=2√2 km h⁻¹, and its true direction is 45° to the horizontal.