Rain appears at 37° with the vertical to a driver moving at 7 m s⁻¹. When the car speed is increased to 25 m s⁻¹, rain again appears at 37° with the vertical on the other side. The true rain velocity is:
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Question

Rain appears at 37° with the vertical to a driver moving at 7 m s⁻¹. When the car speed is increased to 25 m s⁻¹, rain again appears at 37° with the vertical on the other side. The true rain velocity is:

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G1 Physics · Accepted Answer

Let actual rain speed be v, making angle θ with the vertical. Horizontal component = v sinθ. Vertical component = v cosθ. For car speed 7 m s⁻¹: tan37° = (v sinθ-7)/(v cosθ). Using tan37°= 3 4 \frac{3}{4} 4 3 ​ : 4v sinθ-3v cosθ=28. ...(1) For car speed 25 m s⁻¹, apparent rain is on the opposite side: tan37° = (25-v sinθ)/(v cosθ). So 4v sinθ+3v cosθ=100. ...(2) Adding and subtracting: v sinθ=16, v cosθ=12. Therefore v=20 m s⁻¹, tanθ=16/12=4/3 ⇒ θ=53° with vertical.