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Rain is falling at an angle α with respect to the vertical at a velocity of 10 m/s. A girl runs in the opposite direction to the rain at a speed of 8 m/s and observes that the rain appears to make an angle β with the vertical. What is the relationship between α and β?
- tan α = (8 + 10sinβ) / 10cosβ
- tan β = (8 + 10sinα) / 10cosα
- tan α = tan β
- tan α = cot β
Correct answer: tan β = (8 + 10sinα) / 10cosα
Solution
The relative motion of the girl and the rain alters the apparent angle of the rain. Using vector addition, the relationship between α and β is given by tan β = (8 + 10sinα) / 10cosα.
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