A vertical cylindrical container of base area $A$ and upper cross-section area $A_{1}$ , making an angle $30^{o}$ with the horizontal is placed in an open rainy field as show near another cylindrical container having same base area $A$ . Find the ratio of rates of collection of water in the two containers.

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Solution

In first container the Area vector is along the direction of rain. Rate of water collection in first container is $A_{1} \times v e l o c i t y o f r a i n$ .
In second cylinder the component of Area vector along the direction of rain is $A_{1} c o s 60^{o} = A_{1} / 2$ . So, rate of water collection in second container is $0.5 A_{1} \times v e l o c i t y o f r a i n$ .
The ratio of water collection is $2$ .

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A vertical cylindrical container of base area A and upper cross-section area A1, making an angle 30o with the horizontal is placed in an open rainy field as show near another cylindrical container having same base area A. Find the ratio of rates of collection of water in the two containers.